{"id":379,"date":"2025-06-09T09:39:47","date_gmt":"2025-06-09T09:39:47","guid":{"rendered":"https:\/\/ireise.com\/?page_id=379"},"modified":"2025-06-09T15:58:02","modified_gmt":"2025-06-09T15:58:02","slug":"multiple-solutions","status":"publish","type":"page","link":"https:\/\/ireise.com\/index.php\/multiple-solutions\/","title":{"rendered":"\u0415\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u2013 \u043c\u043d\u043e\u0433\u043e \u043f\u043e\u0434\u0445\u043e\u0434\u0438"},"content":{"rendered":"\n<p>\u0412 \u0442\u0430\u043d\u0446\u043e\u0432\u0430 \u0433\u0440\u0443\u043f\u0430 \u0438\u043c\u0430 8 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430 \u0438 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430. \u041f\u043e \u043a\u043e\u043b\u043a\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u043c\u043e\u0436\u0435 \u0434\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u0438\u043c \u0433\u0440\u0443\u043f\u0430 \u043e\u0442 3 \u0442\u0430\u043d\u0446\u044c\u043e\u0440\u0438, \u0432 \u043a\u043e\u044f\u0442\u043e \u0438\u043c\u0430 \u043f\u043e\u043d\u0435 \u0435\u0434\u043d\u043e \u043c\u043e\u043c\u0447\u0435?<br><em>\u0414\u0417\u0418: 28.08. 2020 \u0433. (\u0417\u0430\u0434. 15)<\/em><\/p>\n\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-95dd97fd-c521-42cd-88b8-58da87df0e82\" 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-0-95dd97fd-c521-42cd-88b8-58da87df0e82\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-95dd97fd-c521-42cd-88b8-58da87df0e82\" style=\"color: #000000; \">\u0420\u0435\u0448\u0435\u043d\u0438\u0435 (ChatGPT, 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-0-95dd97fd-c521-42cd-88b8-58da87df0e82\">\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<p>\ud83d\udd37 \u0414\u0430\u0434\u0435\u043d\u043e: <br>\u0412 \u0442\u0430\u043d\u0446\u043e\u0432\u0430\u0442\u0430 \u0433\u0440\u0443\u043f\u0430 \u0438\u043c\u0430:  8 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430 \u0438 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430. \u0422\u044a\u0440\u0441\u0438\u043c <strong>\u0431\u0440\u043e\u044f \u043d\u0430 \u0433\u0440\u0443\u043f\u0438 \u043e\u0442 3 \u0442\u0430\u043d\u0446\u044c\u043e\u0440\u0438<\/strong>, \u0432 \u043a\u043e\u0438\u0442\u043e \u0438\u043c\u0430 <strong>\u043f\u043e\u043d\u0435 \u0435\u0434\u043d\u043e \u043c\u043e\u043c\u0447\u0435<\/strong>.<\/p>\n\n\n\n<p>\ud83d\udd36 \u041f\u043e\u0434\u0445\u043e\u0434: <br>\u0429\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043c\u0435 <strong>\u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0442\u043e \u0441\u044a\u0431\u0438\u0442\u0438\u0435<\/strong>. \u0418\u0441\u043a\u0430\u043c\u0435 \u0434\u0430 \u0438\u0437\u043a\u043b\u044e\u0447\u0438\u043c \u0433\u0440\u0443\u043f\u0438\u0442\u0435, \u043a\u043e\u0438\u0442\u043e \u043d\u0435 \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u0442 \u043c\u043e\u043c\u0447\u0435\u0442\u0430, \u0442.\u0435. \u0442\u0440\u044f\u0431\u0432\u0430 \u0434\u0430 \u043d\u0430\u043c\u0435\u0440\u0438\u043c \u0431\u0440\u043e\u044f \u043d\u0430 \u0433\u0440\u0443\u043f\u0438\u0442\u0435 \u0441\u0430\u043c\u043e \u0441 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430.<\/p>\n\n\n\n<p>1. \u041e\u0431\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u0433\u0440\u0443\u043f\u0438 \u043e\u0442 3 \u0434\u0443\u0448\u0438 (\u0431\u0435\u0437 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f):<br>$$ \\binom{10}{3} = 120 $$ <\/p>\n\n\n\n<p>2. \u041d\u0435\u0432\u0430\u043b\u0438\u0434\u043d\u0438 \u0433\u0440\u0443\u043f\u0438 (\u0441\u0430\u043c\u043e \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430, \u0442.\u0435. 0 \u043c\u043e\u043c\u0447\u0435\u0442\u0430): <br>$$ \\binom{8}{3} = 56 $$<\/p>\n\n\n\n<p>\ud83d\udd38 \u0422\u043e\u0433\u0430\u0432\u0430 \u0431\u0440\u043e\u044f\u0442 \u043d\u0430 \u0433\u0440\u0443\u043f\u0438\u0442\u0435 \u0441 <strong>\u043f\u043e\u043d\u0435 1 \u043c\u043e\u043c\u0447\u0435<\/strong> \u0435: $$ 120 &#8211; 56 = \\boxed{64} $$ <\/p>\n\n\n\n<p>\u2705 \u041e\u0442\u0433\u043e\u0432\u043e\u0440: <strong>64<\/strong> \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0430. <\/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-722871ba-78a4-492c-8fac-35ec65c40e7a\" 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-0-722871ba-78a4-492c-8fac-35ec65c40e7a\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-722871ba-78a4-492c-8fac-35ec65c40e7a\" style=\"color: #000000; \">\u0420\u0435\u0448\u0435\u043d\u0438\u0435 (llama 4, Mistral)<\/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-0-722871ba-78a4-492c-8fac-35ec65c40e7a\">\n\n<p>\u0417\u0430 \u0434\u0430 \u0438\u043c\u0430 \u043f\u043e\u043d\u0435 \u0435\u0434\u043d\u043e \u043c\u043e\u043c\u0447\u0435 \u0432 \u0433\u0440\u0443\u043f\u0430\u0442\u0430 \u043e\u0442 3 \u0442\u0430\u043d\u0446\u044c\u043e\u0440\u0438, \u043c\u043e\u0436\u0435\u043c \u0434\u0430 \u0438\u0437\u0431\u0435\u0440\u0435\u043c \u0438\u043b\u0438 1 \u043c\u043e\u043c\u0447\u0435 \u0438 2 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430, \u0438\u043b\u0438 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430 \u0438 1 \u043c\u043e\u043c\u0438\u0447\u0435. <\/p>\n\n\n\n<p><em>\u0417\u0430 1 \u043c\u043e\u043c\u0447\u0435 \u0438 2 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430 \u0438\u043c\u0430\u043c\u0435<\/em><br>\u0418\u0437\u0431\u0438\u0440\u0430\u043c\u0435 1 \u043c\u043e\u043c\u0447\u0435 \u043e\u0442 2 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043c\u043e\u043c\u0447\u0435\u0442\u0430: $$\\binom{2}{1} = 2$$ \u043d\u0430\u0447\u0438\u043d\u0430.<br>\u0418\u0437\u0431\u0438\u0440\u0430\u043c\u0435 2 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430 \u043e\u0442 8 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430: $$\\binom{8}{2} = 28$$ \u043d\u0430\u0447\u0438\u043d\u0430.<br><strong>\u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 1 \u043c\u043e\u043c\u0447\u0435 \u0438 2 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430<\/strong>: $$2 \\cdot 28 = 56$$ <\/p>\n\n\n\n<p><em>\u0417\u0430 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430 \u0438 1 \u043c\u043e\u043c\u0438\u0447\u0435 \u0438\u043c\u0430\u043c\u0435<\/em><br>\u0418\u0437\u0431\u0438\u0440\u0430\u043c\u0435 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430 \u043e\u0442 2 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043c\u043e\u043c\u0447\u0435\u0442\u0430: $$\\binom{2}{2} = 1$$ \u043d\u0430\u0447\u0438\u043d.<br>\u0418\u0437\u0431\u0438\u0440\u0430\u043c\u0435 1 \u043c\u043e\u043c\u0438\u0447\u0435 \u043e\u0442 8 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u0438 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430: $$\\binom{8}{1} = 8$$ \u043d\u0430\u0447\u0438\u043d\u0430.<br><strong>\u041e\u0431\u0449 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430 \u0438 1 \u043c\u043e\u043c\u0438\u0447\u0435:<\/strong> $$1 \\cdot 8 = 8$$ <br>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u043e, \u043e\u0431\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 \u0433\u0440\u0443\u043f\u0430 \u043e\u0442 3 \u0442\u0430\u043d\u0446\u044c\u043e\u0440\u0438 \u0441 \u043f\u043e\u043d\u0435 \u0435\u0434\u043d\u043e \u043c\u043e\u043c\u0447\u0435 \u0435 $$56 + 8 = 64$$. <\/p>\n\n\n\n<p>\u041e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u043d\u0438\u044f\u0442 \u043e\u0442\u0433\u043e\u0432\u043e\u0440 \u0435 <strong>64<\/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-e9dfa248-49b1-4e99-98f4-9d1f1db1ba8f\" 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-e9dfa248-49b1-4e99-98f4-9d1f1db1ba8f\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e9dfa248-49b1-4e99-98f4-9d1f1db1ba8f\" style=\"color: #000000; \">\u0418\u0437\u0432\u043e\u0434 \u0438 \u0434\u043e\u043f\u044a\u043b\u043d\u0438\u0442\u0435\u043b\u043d\u0438 \u043d\u0430\u0441\u043e\u043a\u0438<\/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-e9dfa248-49b1-4e99-98f4-9d1f1db1ba8f\">\n\n<p>\u041f\u0440\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u0449\u0438 \u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 \u0432\u044a\u043f\u0440\u043e\u0441\u0438: \u201e&#8230; \u043d\u0430\u0439-\u043c\u0430\u043b\u043a\u043e \u0435\u0434\u0438\u043d\u201c, \u201e&#8230; \u043f\u043e\u043d\u0435 \u0435\u0434\u0438\u043d\u201c \u0435 \u043f\u043e-\u043b\u0435\u0441\u043d\u043e \u0434\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0442\u043e \u0441\u044a\u0431\u0438\u0442\u0438\u0435, \u0442.\u0435. \u201e&#8230; \u043d\u0438\u0442\u043e \u0435\u0434\u0438\u043d\u201c.<\/p>\n\n\n\n<p>\u0421\u043b\u0435\u0434\u0432\u0430 \u0434\u0430 \u0441\u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u0437\u0430 \u043f\u044a\u043b\u043d\u0430\u0442\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442 $$ P(A) = 1 \u2013 P(A&#8217;)$$<\/p>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n\n<p class=\"has-text-align-right\"><strong><a href=\"https:\/\/ireise.com\/index.php\/sample-page\/\" data-type=\"page\" data-id=\"2\">Back to Index<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u0442\u0430\u043d\u0446\u043e\u0432\u0430 \u0433\u0440\u0443\u043f\u0430 \u0438\u043c\u0430 8 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430 \u0438 2 \u043c\u043e\u043c\u0447\u0435\u0442\u0430. \u041f\u043e \u043a\u043e\u043b\u043a\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u043c\u043e\u0436\u0435 \u0434\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u0438\u043c \u0433\u0440\u0443\u043f\u0430 \u043e\u0442 3 \u0442\u0430\u043d\u0446\u044c\u043e\u0440\u0438, \u0432 \u043a\u043e\u044f\u0442\u043e \u0438\u043c\u0430 \u043f\u043e\u043d\u0435 \u0435\u0434\u043d\u043e \u043c\u043e\u043c\u0447\u0435?\u0414\u0417\u0418: 28.08. 2020 \u0433. (\u0417\u0430\u0434. 15) Back to Index<\/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-379","page","type-page","status-publish","hentry"],"featured_image_src":null,"_links":{"self":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/379","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=379"}],"version-history":[{"count":15,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/379\/revisions"}],"predecessor-version":[{"id":411,"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/pages\/379\/revisions\/411"}],"wp:attachment":[{"href":"https:\/\/ireise.com\/index.php\/wp-json\/wp\/v2\/media?parent=379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}