{"id":2659,"date":"2022-05-02T14:52:33","date_gmt":"2022-05-02T12:52:33","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kombinacni-cisla-v-pascalove-trojuhelniku-reseny-priklad\/"},"modified":"2022-05-02T18:17:59","modified_gmt":"2022-05-02T16:17:59","slug":"kombinacni-cisla-v-pascalove-trojuhelniku-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kombinacni-cisla-v-pascalove-trojuhelniku-reseny-priklad\/","title":{"rendered":"Kombina\u010dn\u00ed \u010d\u00edsla v Pascalov\u011b troj\u00faheln\u00edku &#8211; \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p>Napi\u0161te dev\u00e1t\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku v obou tvarech.<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Nejprve si mus\u00edme uv\u011bdomit, \u017ee pro dev\u00e1t\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku plat\u00ed, \u017ee <strong><em>n=8<\/em><\/strong> \u21d2 budeme sestavovat \u0159\u00e1dek pro <strong><em>n=8<\/em><\/strong>.<\/p>\n<p>Abychom p\u0159i sepisov\u00e1n\u00ed neud\u011blali chybu, nap\u00ed\u0161eme si obecn\u00fd vzorec platn\u00fd pro ka\u017ed\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku a budeme z n\u011bj vych\u00e1zet.<\/p>\n<p>$$\\binom{n}{0}\\binom{n}{1}\\binom{n}{2}&#8230;&#8230;\\binom{n}{n-2}\\binom{n}{n-1}\\binom{n}{n}$$<\/p>\n<p style=\"text-align: center\">Nyn\u00ed sta\u010d\u00ed pouze dosadit do vzorce. Z\u00edsk\u00e1me:<\/p>\n<p>$$\\binom{8}{0}\\binom{8}{1}\\binom{8}{2}\\binom{8}{3}\\binom{8}{4}\\binom{8}{5}\\binom{8}{6}\\binom{8}{7}\\binom{8}{8}$$<\/p>\n<p style=\"text-align: center\">Jeliko\u017e v\u00edme, jak s kombina\u010dn\u00edmi \u010d\u00edsly pracovat, nen\u00ed nijak slo\u017eit\u00e9 vypo\u010d\u00edtat jednotliv\u00e9 \u010dleny.<\/p>\n<p>$$\\binom{n}{k}=\\frac{n!}{k!(n-k)!}$$<\/p>\n<p>$$\\binom{8}{0}=1$$<\/p>\n<p>$$\\binom{8}{1}=\\frac{8!}{1!7!}=8$$<\/p>\n<p>$$\\binom{8}{2}=\\frac{8!}{2!6!}=28$$<\/p>\n<p>$$\\binom{8}{3}=\\frac{8!}{3!5!}=56$$<\/p>\n<p>$$\\binom{8}{4}=\\frac{8!}{4!4!}=70$$<\/p>\n<p>$$\\binom{8}{5}=\\frac{8!}{5!3!}=56$$<\/p>\n<p>$$\\binom{8}{6}=\\frac{8!}{6!2!}=28$$<\/p>\n<p>$$\\binom{8}{7}=\\frac{8!}{7!1!}=8$$<\/p>\n<p>$$\\binom{8}{8}=1$$<\/p>\n<p>Dev\u00e1t\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku vypad\u00e1:<\/p>\n<p>$$\\binom{8}{0}\\binom{8}{1}\\binom{8}{2}\\binom{8}{3}\\binom{8}{4}\\binom{8}{5}\\binom{8}{6}\\binom{8}{7}\\binom{8}{8}$$<\/p>\n<p style=\"text-align: center\">respektive:<\/p>\n<p>$$1,8,28,56,70,56,28,8,1$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2659","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>Kombina\u010dn\u00ed \u010d\u00edsla v Pascalov\u011b troj\u00faheln\u00edku - \u0159e\u0161en\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\/kombinacni-cisla-v-pascalove-trojuhelniku-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kombina\u010dn\u00ed \u010d\u00edsla v Pascalov\u011b troj\u00faheln\u00edku - \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Napi\u0161te dev\u00e1t\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku v obou tvarech. \u0158e\u0161en\u00ed: Nejprve si mus\u00edme uv\u011bdomit, \u017ee pro dev\u00e1t\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku plat\u00ed, \u017ee n=8 \u21d2 budeme sestavovat \u0159\u00e1dek pro n=8. Abychom p\u0159i sepisov\u00e1n\u00ed neud\u011blali chybu, nap\u00ed\u0161eme si obecn\u00fd vzorec platn\u00fd pro ka\u017ed\u00fd \u0159\u00e1dek Pascalova troj\u00faheln\u00edku a budeme z n\u011bj vych\u00e1zet. $$binom{n}{0}binom{n}{1}binom{n}{2}&#8230;&#8230;binom{n}{n-2}binom{n}{n-1}binom{n}{n}$$ Nyn\u00ed sta\u010d\u00ed pouze dosadit do ... 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