{"id":2437,"date":"2022-04-23T08:09:57","date_gmt":"2022-04-23T08:09:57","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/faktorial-polopate\/"},"modified":"2022-05-01T22:09:23","modified_gmt":"2022-05-01T20:09:23","slug":"faktorial-polopate","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/faktorial-polopate\/","title":{"rendered":"Faktori\u00e1l polopat\u011b"},"content":{"rendered":"<p>Co je faktori\u00e1l? Jak vypad\u00e1? Jak se s n\u00edm po\u010d\u00edt\u00e1? A kdy se v matematice pou\u017e\u00edv\u00e1?<\/p>\n<p>Faktori\u00e1l je nap\u0159\u00edklad toto: <em><strong>5!<\/strong><\/em><\/p>\n<p>Onen vyk\u0159i\u010dn\u00edk neznamen\u00e1, \u017ee si m\u00e1me d\u00e1t na \u010d\u00edslo 5 pozor, ale \u017ee se jedn\u00e1 o faktori\u00e1l p\u011bti. To znamen\u00e1, \u017ee dan\u00fd faktori\u00e1l je <strong>SOU\u010cINEM\u00a0V\u0160ECH P\u0158IROZEN\u00ddCH \u010c\u00cdSEL, KTER\u00c1 JSOU MEN\u0160\u00cd NEBO ROVNA DAN\u00c9MU \u010c\u00cdSLU.<\/strong><\/p>\n<p>Jednodu\u0161e \u0159e\u010deno: <em><strong>5! = 5x4x3x2x1= 120<\/strong><\/em><\/p>\n<p>Z t\u00e9to definice m\u016f\u017eeme snadno odvodit, \u017ee:<\/p>\n<ul>\n<li><strong><em>6!=720 (6x5x4x3x2x1)<\/em><\/strong><\/li>\n<li><strong><em>7!=5040 (7x6x5x4x3x2x1)<\/em><\/strong><\/li>\n<li><strong><em>2!=2 (2&#215;1)<\/em><\/strong><\/li>\n<li><strong><em>1!=1 (1)<\/em><\/strong><\/li>\n<li>ale co <em><strong>0!<\/strong><\/em> ? U n\u011bj si mus\u00edme pamatovat n\u00e1sleduj\u00edc\u00ed rovnost: <strong><em>0!=1<\/em><\/strong><\/li>\n<\/ul>\n<p>Obecn\u011b m\u016f\u017eeme faktori\u00e1l definovat takto: $$(n+1)!=(n+1)\\cdot{n!}$$<\/p>\n<p>Faktori\u00e1l vznikl proto, aby n\u00e1m usnadnil z\u00e1pis. Kdy\u017e tedy po\u010d\u00edt\u00e1me s n\u00e1sobky po sob\u011b jdouc\u00edch p\u0159irozen\u00fdch \u010d\u00edsel, jednodu\u0161e si jejich vypisov\u00e1n\u00ed zkr\u00e1t\u00edme s pou\u017eit\u00edm vyk\u0159i\u010dn\u00edku.<\/p>\n<p>Faktori\u00e1ly maj\u00ed vyu\u017eit\u00ed pr\u00e1v\u011b v kombinatorice, proto se n\u00e1m jejich znalost bude v n\u00e1sleduj\u00edc\u00edch kapitol\u00e1ch hodit.<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2437","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Faktori\u00e1l polopat\u011b | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/faktorial-polopate\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Faktori\u00e1l polopat\u011b | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Co je faktori\u00e1l? 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