{"id":136,"date":"2025-05-23T20:04:57","date_gmt":"2025-05-23T20:04:57","guid":{"rendered":"https:\/\/ireise.com\/?page_id=136"},"modified":"2025-06-06T19:44:41","modified_gmt":"2025-06-06T19:44:41","slug":"problem-chatgpt","status":"publish","type":"page","link":"https:\/\/ireise.com\/index.php\/problem-chatgpt\/","title":{"rendered":"Problem 1"},"content":{"rendered":"\\[\\]\n<p>\u0412 \u043a\u0443\u0442\u0438\u044f \u0438\u043c\u0430: 4 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438, 6 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0438 8 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438.\u00a0\u041a\u0430\u043a\u0432\u0430 \u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442?<br \/><i>\u041f\u0440\u0438\u0435\u043c\u0435\u043d \u0438\u0437\u043f\u0438\u0442 (\u0421\u0423): 02.04.2023 (\u0417\u0430\u0434\u0430\u0447\u0430 7)<\/i><\/p>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-93e26755-a11a-4ba8-8801-fa1b636a815d\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-93e26755-a11a-4ba8-8801-fa1b636a815d\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-93e26755-a11a-4ba8-8801-fa1b636a815d\" style=\"color: #000000; \">\u041d\u0430\u0441\u043e\u043a\u0438 \u0437\u0430 \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-93e26755-a11a-4ba8-8801-fa1b636a815d\">\n\n<p>1. <strong>\u041e\u0431\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438<\/strong> \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u0448 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u0432\u0441\u0438\u0447\u043a\u0438 \u043d\u0430\u043b\u0438\u0447\u043d\u0438 \u2014 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u0437\u0430 \u0431\u0438\u043d\u043e\u043c\u043d\u0438 \u043a\u043e\u0435\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0438: $$\\binom{n}{3}$$<br>\u043a\u044a\u0434\u0435\u0442\u043e \\[n\\] \u0435 \u043e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0442\u043e\u043f\u043a\u0438.<br>2. <strong>\u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438<\/strong>: \u043d\u0430\u043c\u0435\u0440\u0438 \u043f\u043e \u043a\u043e\u043b\u043a\u043e \u043d\u0430\u0447\u0438\u043d\u0430 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0438\u0437\u0431\u0435\u0440\u0430\u0442 <strong>3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449\u0438 \u0446\u0432\u044f\u0442<\/strong> \u2014 \u043d\u0430\u043f\u0440\u0430\u0432\u0438 \u0442\u043e\u0432\u0430 \u043f\u043e\u043e\u0442\u0434\u0435\u043b\u043d\u043e \u0437\u0430 \u0431\u0435\u043b\u0438\u0442\u0435, \u0447\u0435\u0440\u043d\u0438\u0442\u0435 \u0438 \u0437\u0435\u043b\u0435\u043d\u0438\u0442\u0435 (\u0441\u0430\u043c\u043e \u043a\u043e\u0433\u0430\u0442\u043e \u0442\u043e\u0432\u0430 \u0435 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e \u2014 \u0442.\u0435. \u043a\u043e\u0433\u0430\u0442\u043e \u0438\u043c\u0430 \u043f\u043e\u043d\u0435 3 \u043e\u0442 \u0434\u0430\u0434\u0435\u043d \u0446\u0432\u044f\u0442).<br>3. <strong>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442<\/strong>:<\/p>\n\n\n\n<p>$$<br>P = \\frac{\\text{\u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438}}{\\text{\u0412\u0441\u0438\u0447\u043a\u0438}}<br>$$<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-fa4ed8c7-c9dc-4b50-8887-913d88b4d2c4\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-fa4ed8c7-c9dc-4b50-8887-913d88b4d2c4\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fa4ed8c7-c9dc-4b50-8887-913d88b4d2c4\" style=\"color: #000000; \">\u041f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-fa4ed8c7-c9dc-4b50-8887-913d88b4d2c4\">\n\n<p>\u041e\u0431\u0449\u043e:<br>$$<br>4 + 6 + 8 = 18 \\text{\u0442\u043e\u043f\u043a\u0438}<br>$$<br>\u0418\u0437\u0442\u0435\u0433\u043b\u044f\u043c\u0435 <strong>\u043d\u0430 \u0441\u043b\u0443\u0447\u0430\u0435\u043d \u043f\u0440\u0438\u043d\u0446\u0438\u043f 3 \u0442\u043e\u043f\u043a\u0438<\/strong>. \u0422\u044a\u0440\u0441\u0438 \u0441\u0435 <strong>\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0438 \u0442\u0440\u0438\u0442\u0435 \u0434\u0430 \u0441\u0430 \u043e\u0442 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449\u0438 \u0446\u0432\u044f\u0442<\/strong>.<br>\u2705 \u0421\u0442\u044a\u043f\u043a\u0430 1: \u041e\u0431\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u0434\u0430 \u0438\u0437\u0442\u0435\u0433\u043b\u0438\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 18:\n\\[\n\\binom{18}{3} = \\frac{18 \\cdot 17 \\cdot 16}{6} = 816\n\\]\n\u2705 \u0421\u0442\u044a\u043f\u043a\u0430 2: \u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438 (\u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 <strong>\u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449\u0438 \u0446\u0432\u044f\u0442<\/strong>)<br>\ud83c\udfaf (\u0430) 3 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438 (\u043e\u0442 4):<br>$$<br>\\binom{4}{3} = 4<br>$$<br>\ud83c\udfaf (\u0431) 3 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 (\u043e\u0442 6):<br>$$<br>\\binom{6}{3} = 20<br>$$<br>\ud83c\udfaf (\u0432) 3 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 (\u043e\u0442 8):<br>$$<br>\\binom{8}{3} = \\frac{8 \\cdot 7 \\cdot 6}{6} = 56<br>$$<br>\ud83d\udd22 \u041e\u0431\u0449\u043e \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438:<br>$$<br>4 + 20 + 56 = 80<br>$$<br>\u2705 \u0421\u0442\u044a\u043f\u043a\u0430 3: \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442<br>$$<br>P = \\frac{80}{816} = \\frac{10}{102} = \\frac{5}{51}<br>$$<br>\u2705 <strong>\u041e\u0442\u0433\u043e\u0432\u043e\u0440:<\/strong><br>$$<br>\\boxed{\\frac{5}{51}}<br>$$<br>\u0422\u043e\u0432\u0430 \u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438\u0442\u0435 \u0438\u0437\u0442\u0435\u0433\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0441 <strong>\u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442<\/strong>.<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-9dc2c4f9-0403-4a2b-a887-05df39db76be\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-9dc2c4f9-0403-4a2b-a887-05df39db76be\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9dc2c4f9-0403-4a2b-a887-05df39db76be\" style=\"color: #000000; \">Chat GPT<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-9dc2c4f9-0403-4a2b-a887-05df39db76be\">\n\n<p>\u041d\u0435\u043a\u0430 \u0440\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u0441\u0442\u044a\u043f\u043a\u0430 \u043f\u043e \u0441\u0442\u044a\u043f\u043a\u0430.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddfe <strong>\u0414\u0430\u0434\u0435\u043d\u043e:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 <strong>\u0431\u0435\u043b\u0438<\/strong> \u0442\u043e\u043f\u043a\u0438<\/li>\n\n\n\n<li>6 <strong>\u0447\u0435\u0440\u043d\u0438<\/strong> \u0442\u043e\u043f\u043a\u0438<\/li>\n\n\n\n<li>8 <strong>\u0437\u0435\u043b\u0435\u043d\u0438<\/strong> \u0442\u043e\u043f\u043a\u0438<\/li>\n<\/ul>\n\n\n\n<p>\u041e\u0431\u0449\u043e: 4+6+8=18 \u00a0\u0442\u043e\u043f\u043a\u04384 + 6 + 8 = 18 $$text{ \u0442\u043e\u043f\u043a\u0438}$$<\/p>\n\n\n\n<p>\u0418\u0437\u0432\u0430\u0436\u0434\u0430\u043c\u0435 <strong>\u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u043d\u0430 \u0441\u043b\u0443\u0447\u0430\u0435\u043d \u043f\u0440\u0438\u043d\u0446\u0438\u043f<\/strong>. \u0422\u044a\u0440\u0441\u0438\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 <strong>\u0438 \u0442\u0440\u0438\u0442\u0435 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>\u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438<\/strong> \u0434\u0430 \u0438\u0437\u0442\u0435\u0433\u043b\u0438\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 18:<\/h3>\n\n\n\n<p>$$\\binom{18}{3} = \\frac{18 \\cdot 17 \\cdot 16}{6} = 816$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>\u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438<\/strong> \u2014 \u0432\u0441\u0438\u0447\u043a\u0438 \u0442\u043e\u043f\u043a\u0438 \u0441\u0430 \u0441 <strong>\u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449 \u0446\u0432\u044f\u0442<\/strong>:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u27a4 \u0422\u0440\u0438 \u0431\u0435\u043b\u0438 (\u043e\u0442 4):<\/h4>\n\n\n\n<p>$$\\binom{4}{3} = 4$$<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u27a4 \u0422\u0440\u0438 \u0447\u0435\u0440\u043d\u0438 (\u043e\u0442 6):<\/h4>\n\n\n\n<p>$$\\binom{6}{3} = 20$$<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u27a4 \u0422\u0440\u0438 \u0437\u0435\u043b\u0435\u043d\u0438 (\u043e\u0442 8):<\/h4>\n\n\n\n<p>$$\\binom{8}{3} = \\frac{8 \\cdot 7 \\cdot 6}{6} = 56$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 \u041e\u0431\u0449\u043e \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438:<\/h3>\n\n\n\n<p>$$4 + 20 + 56 = 80$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcca <strong>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442:<\/strong><\/h3>\n\n\n\n<p>$$P = \\frac{80}{816} = \\frac{10}{102} = \\boxed{\\frac{5}{51}}$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83c\udfaf <strong>\u041e\u0442\u0433\u043e\u0432\u043e\u0440:<\/strong><\/h3>\n\n\n\n<p>$$\\boxed{\\frac{5}{51}}$$<\/p>\n\n\n\n<p>\u0422\u043e\u0432\u0430 \u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0442\u0435\u0433\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 <strong>\u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442<\/strong>.<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-1-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" style=\"color: #000000; \">DeepSeek<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\">\n\n<p>\u0417\u0430 \u0434\u0430 \u043d\u0430\u043c\u0435\u0440\u0438\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442, \u0449\u0435 \u0441\u043b\u0435\u0434\u0432\u0430\u043c\u0435 \u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 \u0441\u0442\u044a\u043f\u043a\u0438:<\/p>\n\n\n\n<p>1. **\u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0442\u043e\u043f\u043a\u0438 \u0432 \u043a\u0443\u0442\u0438\u044f\u0442\u0430:**<br>&#8211; \u0411\u0435\u043b\u0438: 4<br>&#8211; \u0427\u0435\u0440\u043d\u0438: 6<br>&#8211; \u0417\u0435\u043b\u0435\u043d\u0438: 8<br>&#8211; **\u041e\u0431\u0449\u043e:** 4 + 6 + 8 = 18 \u0442\u043e\u043f\u043a\u0438<\/p>\n\n\n\n<p>2. **\u0411\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u0432\u0441\u0438\u0447\u043a\u0438 (\u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438):**<br>\u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043c\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u0437\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0431\u0435\u0437 \u043f\u043e\u0432\u0442\u043e\u0440\u0435\u043d\u0438\u0435:<br>$$ \\binom{n}{k} = \\frac{n!}{k!(n &#8211; k)!}$$<br><br>\u0422\u0443\u043a \\( n = 18 \\), \\( k = 3 \\):<br>$$\\binom{18}{3} = \\frac{18!}{3! \\cdot 15!} = \\frac{18 \\times 17 \\times 16}{3 \\times 2 \\times 1} = 816$$<br>**\u041e\u0431\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u0438\u0437\u0445\u043e\u0434\u0438:** 816<\/p>\n\n\n\n<p>3. **\u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0438\u0437\u0445\u043e\u0434\u0438 (3 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442):**<br>&#8211; **3 \u0431\u0435\u043b\u0438:** \\( C(4, 3) = \\frac{4!}{3! \\cdot 1!} = 4 \\)<br>(\u0421\u0430\u043c\u043e 4 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438, \u043d\u0435 \u043c\u043e\u0436\u0435 \u043f\u043e\u0432\u0435\u0447\u0435)<br>&#8211; **3 \u0447\u0435\u0440\u043d\u0438:** \\( C(6, 3) = \\frac{6!}{3! \\cdot 3!} = 20 \\)<br>&#8211; **3 \u0437\u0435\u043b\u0435\u043d\u0438:** \\( C(8, 3) = \\frac{8!}{3! \\cdot 5!} = 56 \\)<br>&#8211; **\u041e\u0431\u0449\u043e \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438:** \\( 4 + 20 + 56 = 80 \\)<\/p>\n\n\n\n<p>4. **\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442:**<br>\\[<br>P = \\frac{\\text{\u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0438\u0437\u0445\u043e\u0434\u0438}}{\\text{\u041e\u0431\u0449\u043e \u0438\u0437\u0445\u043e\u0434\u0438}} = \\frac{80}{816} = \\frac{5}{51}<br>\\]<br>\u041e\u043f\u0440\u043e\u0441\u0442\u0435\u043d\u0430 \u0434\u0440\u043e\u0431: \\(\\frac{80 \\div 16}{816 \\div 16} = \\frac{5}{51}\\).<\/p>\n\n\n\n<p>**\u041e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u0435\u043d \u043e\u0442\u0433\u043e\u0432\u043e\u0440:**<br>\\[<br>\\boxed{\\dfrac{5}{51}}<br>\\]<\/p>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-2-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" style=\"color: #000000; \"><\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\"><\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-3-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" style=\"color: #000000; \"><\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\"><\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-699d323e-338d-42d8-93cb-98a9c8d3d12e\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-699d323e-338d-42d8-93cb-98a9c8d3d12e\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-699d323e-338d-42d8-93cb-98a9c8d3d12e\" style=\"color: #000000; \">Mistral AI<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-699d323e-338d-42d8-93cb-98a9c8d3d12e\">\n\n<p>\u0414\u0430 \u043d\u0430\u043c\u0435\u0440\u0438\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0442\u043e\u043f\u043a\u0438<\/h3>\n\n\n\n<p>\u0418\u043c\u0430\u043c\u0435 \u043e\u0431\u0449\u043e (4 + 6 + 8 = 18) \u0442\u043e\u043f\u043a\u0438 \u0432 \u043a\u0443\u0442\u0438\u044f\u0442\u0430.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0442\u043e\u043f\u043a\u0438<\/h3>\n\n\n\n<p>\u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u043d\u0430\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 18 \u0441\u0435 \u0438\u0437\u0447\u0438\u0441\u043b\u044f\u0432\u0430 \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u0437\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438:<br>$$<br>C(n, k) = \\frac{n!}{k!(n-k)!}<br>$$<br>\u043a\u044a\u0434\u0435\u0442\u043e (n = 18) \u0438 (k = 3):<br>$$<br>C(18, 3) = \\frac{18!}{3!(18-3)!} = \\frac{18 \\times 17 \\times 16}{3 \\times 2 \\times 1} = 816<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u0411\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438<\/h3>\n\n\n\n<p>\u0422\u0440\u044f\u0431\u0432\u0430 \u0434\u0430 \u043d\u0430\u043c\u0435\u0440\u0438\u043c \u0431\u0440\u043e\u044f \u043d\u0430 \u043d\u0430\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449 \u0446\u0432\u044f\u0442.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0411\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438<\/strong>: \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u043d\u0430\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 4 \u0435:<br>$$<br>C(4, 3) = \\frac{4!}{3!(4-3)!} = 4<br>$$<\/li>\n\n\n\n<li><strong>\u0427\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438<\/strong>: \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u043d\u0430\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 6 \u0435:<br>$$<br>C(6, 3) = \\frac{6!}{3!(6-3)!} = 20<br>$$<\/li>\n\n\n\n<li><strong>\u0417\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438<\/strong>: \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u043d\u0430\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 3 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 8 \u0435:<br>$$<br>C(8, 3) = \\frac{8!}{3!(8-3)!} = 56<br>$$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438<\/h3>\n\n\n\n<p>\u041e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438 \u0435 \u0441\u0443\u043c\u0430\u0442\u0430 \u043e\u0442 \u0433\u043e\u0440\u043d\u0438\u0442\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438:<br>\\[<br>4 + 20 + 56 = 80<br>\\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5. \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442<\/h3>\n\n\n\n<p>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438\u0442\u0435 \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442 \u0435:<br>\\[<br>\\frac{80}{816} = \\frac{5}{51} \\approx 0.098<br>\\]<\/p>\n\n\n\n<p>\u0422\u0430\u043a\u0430, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u043d\u043e (9.8\\%).<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-5-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\" style=\"color: #000000; \"><\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-9cd90e89-6a7d-42d1-bfb3-fcb75d6594fb\"><\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-c631aa98-a9cf-40c2-a72d-bd2c8e99ed86\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-c631aa98-a9cf-40c2-a72d-bd2c8e99ed86\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c631aa98-a9cf-40c2-a72d-bd2c8e99ed86\" style=\"color: #000000; \">DeepAI Math AI<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-c631aa98-a9cf-40c2-a72d-bd2c8e99ed86\">\n\n<p>\u0420\u0430\u0437\u0431\u0438\u0440\u0430\u043c, \u0447\u0435 \u0438\u0441\u043a\u0430\u0448 \u0434\u0430 \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442. \u041d\u0435\u043a\u0430 \u043f\u0440\u0435\u043c\u0438\u043d\u0435\u043c \u0441\u0442\u044a\u043f\u043a\u0430 \u043f\u043e \u0441\u0442\u044a\u043f\u043a\u0430.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u0442\u044a\u043f\u043a\u0430 1: \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0442\u043e\u043f\u043a\u0438<\/h3>\n\n\n\n<p>\u0412 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0438\u043c\u0430\u043c\u0435:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 \u0431\u0435\u043b\u0438<\/li>\n\n\n\n<li>6 \u0447\u0435\u0440\u043d\u0438<\/li>\n\n\n\n<li>8 \u0437\u0435\u043b\u0435\u043d\u0438<\/li>\n<\/ul>\n\n\n\n<p>\u041e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0442\u043e\u043f\u043a\u0438 \u0435:<br>[ 4 + 6 + 8 = 18 ]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u0442\u044a\u043f\u043a\u0430 2: \u041e\u0431\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u0442\u043e\u043f\u043a\u0438<\/h3>\n\n\n\n<p>\u0422\u043e\u0432\u0430 \u0435 \u0431\u0440\u043e\u044f\u0442 \u043d\u0430 \u0432\u0441\u0438\u0447\u043a\u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438, \u0441 \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 18. \u0422\u043e\u0432\u0430 \u0441\u0435 \u0438\u0437\u0447\u0438\u0441\u043b\u044f\u0432\u0430 \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u0437\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438:<br>[ C(n, k) = \\frac{n!}{k!(n-k)!} ]<\/p>\n\n\n\n<p>\u0422\u0443\u043a:<br>[ C(18, 3) = \\frac{18!}{3!(18-3)!} = \\frac{18 \\times 17 \\times 16}{3 \\times 2 \\times 1} = 816 ]<\/p>\n\n\n\n<p>\u0422\u043e\u0432\u0430 \u0435 \u043e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u0442\u043e\u043f\u043a\u0438.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u0442\u044a\u043f\u043a\u0430 3: \u0411\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u0438\u043d \u0446\u0432\u044f\u0442<\/h3>\n\n\n\n<p>\u0422\u0440\u044f\u0431\u0432\u0430 \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u0435\u0434\u0438\u043d \u0446\u0432\u044f\u0442, \u043a\u0430\u0442\u043e:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0437\u0430 \u0431\u0435\u043b\u0438: \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c \u0432\u0441\u0438\u0447\u043a\u0438 3, \u0430\u043a\u043e \u0438\u043c\u0430 \u043f\u043e\u043d\u0435 3 \u0431\u0435\u043b\u0438 (\u0430 \u0438\u043c\u0430\u043c\u0435 \u0441\u0430\u043c\u043e 4, \u0442\u0430\u043a\u0430 \u0447\u0435 \u0435 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e):<br>[ C(4, 3) = 4 ]<\/li>\n\n\n\n<li>\u0437\u0430 \u0447\u0435\u0440\u043d\u0438: \u0438\u043c\u0430\u043c\u0435 6 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438:<br>[ C(6, 3) = 20 ]<\/li>\n\n\n\n<li>\u0437\u0430 \u0437\u0435\u043b\u0435\u043d\u0438: \u0438\u043c\u0430\u043c\u0435 8 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438:<br>[ C(8, 3) = 56 ]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u0442\u044a\u043f\u043a\u0430 4: \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 \u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u0438\u043d \u0446\u0432\u044f\u0442<\/h3>\n\n\n\n<p>\u041e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c \u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442 \u0435 \u0441\u0443\u043c\u0430 \u043d\u0430 \u0432\u0441\u0438\u0447\u043a\u0438 \u0442\u0435\u0437\u0438 \u0441\u043b\u0443\u0447\u0430\u0438:<br>[ 4 + 20 + 56 = 80 ]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u0442\u044a\u043f\u043a\u0430 5: \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442<\/h3>\n\n\n\n<p>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u0438\u043d \u0446\u0432\u044f\u0442 \u0435:<br>[ \\text{\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442} = \\frac{\\text{\u0431\u0440\u043e\u0439 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438}}{\\text{\u043e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438}} = \\frac{80}{816} ]<\/p>\n\n\n\n<p>\u041c\u043e\u0436\u0435\u043c \u0434\u0430 \u043e\u043f\u0440\u043e\u0441\u0442\u0438\u043c \u0434\u0440\u043e\u0431\u0442\u0430:<br>[ \\frac{80}{816} = \\frac{10}{102} = \\frac{5}{51} ]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u041e\u0442\u0433\u043e\u0432\u043e\u0440:<\/strong><\/h3>\n\n\n\n<p>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u0438\u043d \u0446\u0432\u044f\u0442 \u0435 <strong>(\\frac{5}{51})<\/strong>.<\/p>\n\n\n\n<p>\u0410\u043a\u043e \u0438\u043c\u0430\u0448 \u0432\u044a\u043f\u0440\u043e\u0441\u0438 \u0438\u043b\u0438 \u0438\u0441\u043a\u0430\u0448 \u043e\u0449\u0435 \u043e\u0431\u044f\u0441\u043d\u0435\u043d\u0438\u044f, \u043d\u0435 \u0441\u0435 \u043a\u043e\u043b\u0435\u0431\u0430\u0439 \u0434\u0430 \u043f\u0438\u0442\u0430\u0448!<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-eeb22ce7-0dde-454b-81c1-cb79a8c3d00e\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1;\" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-eeb22ce7-0dde-454b-81c1-cb79a8c3d00e\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-eeb22ce7-0dde-454b-81c1-cb79a8c3d00e\" style=\"color: #000000; \">YesChat.AI<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-eeb22ce7-0dde-454b-81c1-cb79a8c3d00e\">\n\n<p>\u0414\u0430 \u0440\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u0441\u0442\u044a\u043f\u043a\u0430 \u043f\u043e \u0441\u0442\u044a\u043f\u043a\u0430: ### \u0421\u0442\u044a\u043f\u043a\u0430 1: \u041e\u0431\u0449\u043e \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0442\u043e\u043f\u043a\u0438 \u0412 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0438\u043c\u0430 \u043e\u0431\u0449\u043e: &#8211; 4 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438, &#8211; 6 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438, &#8211; 8 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438. \u041e\u0431\u0449\u043e \u0442\u043e\u043f\u043a\u0438 = 4 + 6 + 8 = **18 \u0442\u043e\u043f\u043a\u0438**. ### \u0421\u0442\u044a\u043f\u043a\u0430 2: \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438\u0442\u0435 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f \u043d\u0430 3 \u0442\u043e\u043f\u043a\u0438 \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u0432\u0441\u0438\u0447\u043a\u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438, \u043f\u043e \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0432\u0430\u0434\u0438\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u043e\u0431\u0449\u043e 18 \u0435 \u0434\u0430\u0434\u0435\u043d \u043e\u0442 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f\u0442\u0430: \\[ C(18, 3) = \\frac{18 \\times 17 \\times 16}{3 \\times 2 \\times 1} = 816 \\] ### \u0421\u0442\u044a\u043f\u043a\u0430 3: \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438\u0442\u0435 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f (\u0441 \u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449 \u0446\u0432\u044f\u0442) \u0422\u043e\u0432\u0430 \u043e\u0437\u043d\u0430\u0447\u0430\u0432\u0430, \u0447\u0435 \u0432\u0441\u0438\u0447\u043a\u0438 \u0442\u0440\u0438 \u0442\u043e\u043f\u043a\u0438 \u0442\u0440\u044f\u0431\u0432\u0430 \u0434\u0430 \u0441\u0430 \u043e\u0442 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449\u0438 \u0446\u0432\u044f\u0442. \u0429\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043c\u0435 \u043f\u043e\u043e\u0442\u0434\u0435\u043b\u043d\u043e \u0432\u0441\u044f\u043a\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442: #### 1. \u0422\u0440\u0438 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438: \u041e\u0442 4 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438 \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u043f\u043e \u0441\u043b\u0435\u0434\u043d\u0438\u044f \u043d\u0430\u0447\u0438\u043d: \\[ C(4, 3) = \\frac{4 \\times 3 \\times 2}{3 \\times 2 \\times 1} = 4 \\] #### 2. \u0422\u0440\u0438 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438: \u041e\u0442 6 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u043f\u043e \u0441\u043b\u0435\u0434\u043d\u0438\u044f \u043d\u0430\u0447\u0438\u043d: \\[ C(6, 3) = \\frac{6 \\times 5 \\times 4}{3 \\times 2 \\times 1} = 20 \\] #### 3. \u0422\u0440\u0438 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438: \u041e\u0442 8 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c 3 \u043f\u043e \u0441\u043b\u0435\u0434\u043d\u0438\u044f \u043d\u0430\u0447\u0438\u043d: \\[ C(8, 3) = \\frac{8 \\times 7 \\times 6}{3 \\times 2 \\times 1} = 56 \\] ### \u0421\u0442\u044a\u043f\u043a\u0430 4: \u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f \u041e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f \u0435 \u0441\u0443\u043c\u0430\u0442\u0430 \u043e\u0442 \u0431\u0440\u043e\u044f \u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0437\u0430 \u0432\u0441\u044f\u043a\u0430 \u043e\u0442 \u0442\u0440\u0438\u0442\u0435 \u043a\u0430\u0442\u0435\u0433\u043e\u0440\u0438\u0438 \u0442\u043e\u043f\u043a\u0438: \\[ 4 \\, (\\text{\u0431\u0435\u043b\u0438}) + 20 \\, (\\text{\u0447\u0435\u0440\u043d\u0438}) + 56 \\, (\\text{\u0437\u0435\u043b\u0435\u043d\u0438}) = 80 \\] ### \u0421\u0442\u044a\u043f\u043a\u0430 5: \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442 \u041d\u0430\u043a\u0440\u0430\u044f, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0434\u0430 \u0438\u0437\u0432\u0430\u0434\u0438\u043c 3 \u0442\u043e\u043f\u043a\u0438 \u0441 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449 \u0446\u0432\u044f\u0442 \u0435: \\[ P = \\frac{\\text{\u0431\u043b\u0430\u0433\u043e\u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f}}{\\text{\u0432\u0441\u0438\u0447\u043a\u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u0438\u0437\u0432\u0430\u0436\u0434\u0430\u043d\u0438\u044f}} = \\frac{80}{816} \\] \u041c\u043e\u0436\u0435\u043c \u0434\u0430 \u043e\u043f\u0440\u043e\u0441\u0442\u0438\u043c \u0434\u0440\u043e\u0431\u0442\u0430: \\[ P = \\frac{10}{102} \\] \u0438\u043b\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u043d\u043e: \\[ P \\approx 0.098 \\] \u0422\u0430\u043a\u0430 \u0447\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442 \u0435 **\u043e\u043a\u043e\u043b\u043e 9.8%**.<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u0412 \u043a\u0443\u0442\u0438\u044f \u0438\u043c\u0430: 4 \u0431\u0435\u043b\u0438 \u0442\u043e\u043f\u043a\u0438, 6 \u0447\u0435\u0440\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u0438 8 \u0437\u0435\u043b\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438.\u00a0\u041a\u0430\u043a\u0432\u0430 \u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0442\u0430 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0438\u0437\u0432\u0430\u0434\u0435\u043d\u0438 \u0442\u043e\u043f\u043a\u0438 \u043e\u0442 \u043a\u0443\u0442\u0438\u044f\u0442\u0430 \u0434\u0430 \u0441\u0430 \u0441 \u0435\u0434\u043d\u0430\u043a\u044a\u0432 \u0446\u0432\u044f\u0442?\u041f\u0440\u0438\u0435\u043c\u0435\u043d \u0438\u0437\u043f\u0438\u0442 (\u0421\u0423): 02.04.2023 (\u0417\u0430\u0434\u0430\u0447\u0430 7)<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ub_ctt_via":"","footnotes":""},"class_list":["post-136","page","type-page","status-publish","hentry"],"featured_image_src":null,"_links":{"self":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/comments?post=136"}],"version-history":[{"count":91,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions"}],"predecessor-version":[{"id":339,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions\/339"}],"wp:attachment":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/media?parent=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}