{"id":2454,"date":"2022-04-25T13:10:30","date_gmt":"2022-04-25T13:10:30","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/variace-bez-opakovani-zakladni-vzorce-vzorovy-priklad\/"},"modified":"2022-04-25T16:43:53","modified_gmt":"2022-04-25T16:43:53","slug":"variace-bez-opakovani-zakladni-vzorce-vzorovy-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/variace-bez-opakovani-zakladni-vzorce-vzorovy-priklad\/","title":{"rendered":"Variace bez opakov\u00e1n\u00ed &#8211; z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>Kdy vyu\u017e\u00edt vzore\u010dku pro v\u00fdpo\u010det VARIAC\u00cd BEZ OPAKOV\u00c1N\u00cd a jak se v\u016fbec po\u010d\u00edtaj\u00ed?<\/p>\n<ul>\n<li>Variace bez opakov\u00e1n\u00ed vyu\u017eijeme v p\u0159\u00edpad\u011b, kdy m\u00e1me vyb\u00edrat n\u011bjak\u00e9 prvky u kter\u00fdch <strong>Z\u00c1LE\u017d\u00cd NA PO\u0158AD\u00cd A NESM\u00cdME DVAKR\u00c1T POU\u017d\u00cdT STEJN\u00dd PRVEK<\/strong><\/li>\n<li>P\u0159\u00edklady na Variace bez opakov\u00e1n\u00ed mohou b\u00fdt nap\u0159\u00edklad: rozd\u011blen\u00ed medail\u00ed, po\u010det kombinac\u00ed k sejfu,<\/li>\n<li>Z <strong><em>n<\/em><\/strong> prvk\u016f v\u017edy vyb\u00edr\u00e1me <em><strong>k<\/strong><\/em> kombinac\u00ed, proto vzorec k v\u00fdpo\u010dtu Variac\u00ed bez opakov\u00e1n\u00ed vypad\u00e1 n\u00e1sledovn\u011b:<\/li>\n<\/ul>\n<p>$$V(k,n)=\\frac{n!}{(n-k)!}$$<\/p>\n<p style=\"text-align: center\">neboli<\/p>\n<p>$$V(k,n)=n(n-1)(n-2)&#8230;.(n-k+1)$$<\/p>\n<ul>\n<li>ze vzorce a z toho co <em><strong>n<\/strong><\/em> a <strong><em>k\u00a0<\/em><\/strong>p\u0159edstavuj\u00ed je jasn\u00e9, \u017ee <strong><em>k\u2264n<\/em><\/strong><\/li>\n<\/ul>\n<p><strong>Vzorov\u00fd p\u0159\u00edklad:<\/strong><\/p>\n<p>Chce\u0161 si vyrobit vlastn\u00ed vlajku, kter\u00e1 bude slo\u017eena ze t\u0159\u00ed barevn\u00fdch pruh\u016f. K dispozici m\u00e1\u0161 celkem 5 barev (\u017elutou, modrou, zelenou, b\u00edlou a \u010dernou). Vypo\u010d\u00edtej, kolik r\u016fzn\u00fdch vlajek si m\u016f\u017ee\u0161 vyrobit.<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Vyb\u00edrat m\u016f\u017ee\u0161 z p\u011bti barev \u21d2 <em><strong>n=5\u00a0<\/strong><\/em>a celkem tvo\u0159\u00ed\u0161 variaci o t\u0159ech prvc\u00edch \u21d2<strong><em> k=3<\/em><\/strong><\/p>\n<p>Sta\u010d\u00ed tedy dosadit do vzorce:<\/p>\n<p>$$V(k,n)=\\frac{n!}{(n-k)!}$$<\/p>\n<p>$$V(3,5)=\\frac{5!}{(5-3)!}=\\frac{5!}{2!}=\\frac{5\\cdot{4}\\cdot{3}\\cdot{2}\\cdot{1}}{2\\cdot{1}}=5\\cdot{4}\\cdot{3}=60$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2454","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>Variace bez opakov\u00e1n\u00ed - z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad | 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\/variace-bez-opakovani-zakladni-vzorce-vzorovy-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Variace bez opakov\u00e1n\u00ed - z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Kdy vyu\u017e\u00edt vzore\u010dku pro v\u00fdpo\u010det VARIAC\u00cd BEZ OPAKOV\u00c1N\u00cd a jak se v\u016fbec po\u010d\u00edtaj\u00ed? Variace bez opakov\u00e1n\u00ed vyu\u017eijeme v p\u0159\u00edpad\u011b, kdy m\u00e1me vyb\u00edrat n\u011bjak\u00e9 prvky u kter\u00fdch Z\u00c1LE\u017d\u00cd NA PO\u0158AD\u00cd A NESM\u00cdME DVAKR\u00c1T POU\u017d\u00cdT STEJN\u00dd PRVEK P\u0159\u00edklady na Variace bez opakov\u00e1n\u00ed mohou b\u00fdt nap\u0159\u00edklad: rozd\u011blen\u00ed medail\u00ed, po\u010det kombinac\u00ed k sejfu, Z n prvk\u016f v\u017edy vyb\u00edr\u00e1me k ... 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Variace bez opakov\u00e1n\u00ed vyu\u017eijeme v p\u0159\u00edpad\u011b, kdy m\u00e1me vyb\u00edrat n\u011bjak\u00e9 prvky u kter\u00fdch Z\u00c1LE\u017d\u00cd NA PO\u0158AD\u00cd A NESM\u00cdME DVAKR\u00c1T POU\u017d\u00cdT STEJN\u00dd PRVEK P\u0159\u00edklady na Variace bez opakov\u00e1n\u00ed mohou b\u00fdt nap\u0159\u00edklad: rozd\u011blen\u00ed medail\u00ed, po\u010det kombinac\u00ed k sejfu, Z n prvk\u016f v\u017edy vyb\u00edr\u00e1me k ... 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