{"id":1760218,"date":"2026-05-21T11:45:00","date_gmt":"2026-05-21T14:45:00","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=1760218"},"modified":"2026-05-19T12:23:29","modified_gmt":"2026-05-19T15:23:29","slug":"combinacao","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/combinacao\/","title":{"rendered":"Combina\u00e7\u00e3o"},"content":{"rendered":"\n<p class=\"has-medium-font-size\">Aprenda os conceitos essenciais para a resolu\u00e7\u00e3o de quest\u00f5es sobre combina\u00e7\u00e3o com um resumo para as principais provas de concursos.<\/p>\n\n\n\n<p>Ol\u00e1, pessoal! Tudo bem com voc\u00eas?<\/p>\n\n\n\n<p>A <strong>combina\u00e7\u00e3o<\/strong> \u00e9 um dos conceitos centrais da <strong>an\u00e1lise combinat\u00f3ria<\/strong> e aparece com frequ\u00eancia em quest\u00f5es que envolvem <strong>escolha de elementos sem considerar a ordem<\/strong>. Diferente do arranjo e da permuta\u00e7\u00e3o, aqui o foco est\u00e1 apenas na sele\u00e7\u00e3o, e n\u00e3o na organiza\u00e7\u00e3o.<\/p>\n\n\n\n<p>Em provas de bancas como <strong><\/strong><strong><a href=\"https:\/\/conhecimento.fgv.br\/concursos\" target=\"_blank\" rel=\"noreferrer noopener\">FGV<\/a>, <a href=\"https:\/\/www.concursosfcc.com.br\/\" target=\"_blank\" rel=\"noreferrer noopener\">FCC<\/a><\/strong> <strong>e<\/strong> <a href=\"https:\/\/www.cebraspe.org.br\/concursos\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Cebraspe<\/strong><\/a>, \u00e9 comum encontrar problemas em que o candidato precisa distinguir rapidamente entre <strong>arranjo, permuta\u00e7\u00e3o e combina\u00e7\u00e3o<\/strong>, sendo essa diferencia\u00e7\u00e3o uma das maiores fontes de erro.<\/p>\n\n\n\n<p>Neste artigo, voc\u00ea vai entender o conceito de combina\u00e7\u00e3o, suas aplica\u00e7\u00f5es e como resolver quest\u00f5es com seguran\u00e7a, com exemplos comentados.<\/p>\n\n\n\n<p><strong>Confira os t\u00f3picos que ser\u00e3o abordados:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O que \u00e9 combina\u00e7\u00e3o;<\/li>\n\n\n\n<li>Combina\u00e7\u00e3o simples;<\/li>\n\n\n\n<li>Combina\u00e7\u00e3o composta;<\/li>\n\n\n\n<li>Exemplos resolvidos;<\/li>\n\n\n\n<li>Resumo.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-combinacao\">Combina\u00e7\u00e3o<\/h2>\n\n\n\n<p>Combina\u00e7\u00e3o \u00e9 o processo de <strong>escolher elementos de um conjunto, sem se preocupar com a ordem<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-ideia-central\"><strong>Ideia central<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Escolhemos alguns elementos;<\/li>\n\n\n\n<li>A ordem n\u00e3o importa.<\/li>\n<\/ul>\n\n\n\n<p>Por exemplo, escolhendo 2 elementos entre A, B e C:<\/p>\n\n\n\n<p class=\"has-text-align-center\">AB, AC, BC<\/p>\n\n\n\n<p>Note que AB e BA representam a mesma escolha.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-areas-e-aplicacoes\"><strong>\u00c1reas e aplica\u00e7\u00f5es<\/strong><\/h3>\n\n\n\n<p>A combina\u00e7\u00e3o aparece em diversas situa\u00e7\u00f5es pr\u00e1ticas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Forma\u00e7\u00e3o de comiss\u00f5es;<\/li>\n\n\n\n<li>Escolha de grupos;<\/li>\n\n\n\n<li>Sele\u00e7\u00e3o de equipes;<\/li>\n\n\n\n<li>Loterias e jogos.<\/li>\n<\/ul>\n\n\n\n<p><strong><em>Dica<\/em><\/strong><strong>:<\/strong> sempre que houver <strong>escolha sem ordem<\/strong>, pense em combina\u00e7\u00e3o.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-combinacao-simples\">Combina\u00e7\u00e3o Simples<\/h2>\n\n\n\n<p>A combina\u00e7\u00e3o simples ocorre quando <strong>n\u00e3o h\u00e1 restri\u00e7\u00f5es adicionais al\u00e9m da escolha<\/strong>.<\/p>\n\n\n\n<p><strong>F\u00f3rmula<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"140\" height=\"53\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110714\/image-36.png\" alt=\"Combina\u00e7\u00e3o simples\" class=\"wp-image-1760219\"\/><\/figure>\n\n\n\n<p>Onde:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>n = total de elementos dispon\u00edveis;<\/li>\n\n\n\n<li>p = quantidade de elementos escolhidos;<\/li>\n\n\n\n<li>n! (fatorial de n) = n \u00d7 (n &#8211; 1) \u00d7 (n &#8211; 2) \u00d7 &#8230; \u00d7 1.<\/li>\n<\/ul>\n\n\n\n<p><strong>Exemplo<\/strong><\/p>\n\n\n\n<p>De quantas formas podemos escolher 2 pessoas dentre 5?<\/p>\n\n\n\n<p>Resolu\u00e7\u00e3o: como a ordem n\u00e3o importa, usamos a combina\u00e7\u00e3o.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"50\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110727\/image-37.png\" alt=\"Exemplo resolvido\" class=\"wp-image-1760220\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110727\/image-37.png 323w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110727\/image-37-300x46.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110727\/image-37-150x23.png 150w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<p>Portanto, podemos escolher de <strong>10 formas<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-combinacao-composta\">Combina\u00e7\u00e3o Composta<\/h2>\n\n\n\n<p>Por outro lado, a composta ocorre quando o problema envolve <strong>mais de uma escolha ou etapas sucessivas<\/strong>.<\/p>\n\n\n\n<p><strong>Exemplo<\/strong><\/p>\n\n\n\n<p>Uma empresa possui 6 homens e 4 mulheres. De quantas formas podemos formar uma equipe com 2 homens e 1 mulher?<\/p>\n\n\n\n<p>Resolu\u00e7\u00e3o: a quest\u00e3o envolve duas escolhas independentes.<\/p>\n\n\n\n<p>1) Escolher 2 homens:<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>6,2<\/sub> = 15<\/p>\n\n\n\n<p>2) Escolher 1 mulher:<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>4,1<\/sub> = 4<\/p>\n\n\n\n<p>Total:<\/p>\n\n\n\n<p class=\"has-text-align-center\">15 \u00d7 4 = 60<\/p>\n\n\n\n<p>Portanto, <strong>60 formas<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-exemplos-resolvidos\">Exemplos Resolvidos<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-1\"><strong>Exemplo 1<\/strong><\/h3>\n\n\n\n<p>Em um jogo, o jogador deve escolher 6 n\u00fameros entre 10. Quantas combina\u00e7\u00f5es s\u00e3o poss\u00edveis?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p>A ordem dos n\u00fameros n\u00e3o importa, apenas a escolha. Logo:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"54\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110823\/image-38.png\" alt=\"Exemplo resolvido\" class=\"wp-image-1760221\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110823\/image-38.png 205w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/06110823\/image-38-150x40.png 150w\" sizes=\"auto, (max-width: 205px) 100vw, 205px\" \/><\/figure>\n\n\n\n<p>Portanto, s\u00e3o poss\u00edveis <strong>210 combina\u00e7\u00f5es<\/strong> diferentes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-2\"><strong>Exemplo 2<\/strong><\/h3>\n\n\n\n<p>Uma equipe deve ser formada com 3 pessoas dentre 8, sendo que duas pessoas espec\u00edficas n\u00e3o podem ficar juntas. Quantas equipes s\u00e3o poss\u00edveis?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p>Aqui, devemos aplicar combina\u00e7\u00e3o com <strong>restri\u00e7\u00e3o<\/strong>.<\/p>\n\n\n\n<p>1) Total sem restri\u00e7\u00e3o:<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>8,3<\/sub> = 56<\/p>\n\n\n\n<p>2) Casos proibidos (dupla fixa + 1 pessoa):<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>6,1<\/sub> = 6<\/p>\n\n\n\n<p>3) Total v\u00e1lido (retirando os casos restritos):<\/p>\n\n\n\n<p class=\"has-text-align-center\">56 &#8211; 6 = 50<\/p>\n\n\n\n<p>Portanto, h\u00e1 <strong>50 equipes<\/strong> poss\u00edveis.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-3\"><strong>Exemplo 3<\/strong><\/h3>\n\n\n\n<p>Uma empresa possui 5 engenheiros e 3 analistas. Quantas equipes de 4 pessoas podem ser formadas com exatamente 2 engenheiros?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p>Aqui, devemos utilizar combina\u00e7\u00e3o composta com <strong>m\u00faltiplas etapas<\/strong>.<\/p>\n\n\n\n<p>1) Escolher 2 engenheiros:<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>5,2<\/sub> = 10<\/p>\n\n\n\n<p>2) Escolher 2 analistas:<\/p>\n\n\n\n<p class=\"has-text-align-center\">C<sub>3,2<\/sub> = 3<\/p>\n\n\n\n<p>3) Total:<\/p>\n\n\n\n<p class=\"has-text-align-center\">10 \u00d7 3 = 30<\/p>\n\n\n\n<p>Portanto, podem ser formadas <strong>30 equipes<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-resumo-combinacao\">Resumo \u2013 Combina\u00e7\u00e3o<\/h2>\n\n\n\n<p>Para te ajudar a revisar os principais pontos que vimos at\u00e9 aqui sobre combina\u00e7\u00e3o, de forma r\u00e1pida e estrat\u00e9gica, preparamos um resumo:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Tipo de combina\u00e7\u00e3o<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Quando usar<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>F\u00f3rmula<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Palavras-chave t\u00edpicas<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Combina\u00e7\u00e3o simples<\/td><td class=\"has-text-align-center\" data-align=\"center\">Escolha sem ordem (ordem n\u00e3o importa)<\/td><td class=\"has-text-align-center\" data-align=\"center\">n! \/ (p! (n-p)!)<\/td><td class=\"has-text-align-center\" data-align=\"center\">grupo, comiss\u00e3o, equipe<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Combina\u00e7\u00e3o composta<\/td><td class=\"has-text-align-center\" data-align=\"center\">M\u00faltiplas escolhas<\/td><td class=\"has-text-align-center\" data-align=\"center\">Multiplica\u00e7\u00e3o de combina\u00e7\u00f5es<\/td><td class=\"has-text-align-center\" data-align=\"center\">etapas, restri\u00e7\u00f5es, categorias<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-finalizando\">Finalizando<\/h2>\n\n\n\n<p>A combina\u00e7\u00e3o \u00e9 uma ferramenta essencial para resolver problemas em que precisamos selecionar elementos sem considerar a ordem. O ponto central est\u00e1 em identificar corretamente esse aspecto no enunciado.<\/p>\n\n\n\n<p>Muitos erros em prova acontecem quando o candidato confunde  a utiliza\u00e7\u00e3o com arranjo, aplicando f\u00f3rmulas de forma equivocada. Por isso, desenvolver o h\u00e1bito de analisar o papel da ordem no problema \u00e9 fundamental.<\/p>\n\n\n\n<p>Com <strong>pr\u00e1tica<\/strong>, esse reconhecimento se torna autom\u00e1tico, permitindo resolver quest\u00f5es com mais rapidez e seguran\u00e7a. Dominar combina\u00e7\u00e3o completa o conjunto de ferramentas b\u00e1sicas da an\u00e1lise combinat\u00f3ria e contribui diretamente para um melhor desempenho em provas.<\/p>\n\n\n\n<p>\u00c9 importante refor\u00e7ar que este conte\u00fado <strong>deve ser utilizado como complemento ao material em PDF<\/strong>, onde a abordagem \u00e9 aprofundada e completa. Al\u00e9m disso, \u00e9 fundamental praticar com muitas quest\u00f5es, preferencialmente separadas por banca, para entender as diferentes formas de cobran\u00e7a.<\/p>\n\n\n\n<p>Quer se aprofundar no tema? O Estrat\u00e9gia Concursos disponibiliza <strong>materiais em PDF completos e atualizados<\/strong>, com teoria detalhada, quest\u00f5es comentadas e videoaulas direcionadas para cada concurso. Com pr\u00e1tica e um bom material, voc\u00ea estar\u00e1 preparado para resolver qualquer quest\u00e3o que aparecer na sua prova.<\/p>\n\n\n\n<p>Acesse <a href=\"https:\/\/www.estrategiaconcursos.com.br\/\" target=\"_blank\" rel=\"noreferrer noopener\">os cursos do Estrat\u00e9gia Concursos<\/a> e fortale\u00e7a sua prepara\u00e7\u00e3o com um conte\u00fado de alto n\u00edvel.<\/p>\n\n\n\n<p>Bons estudos e at\u00e9 a pr\u00f3xima!<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\" id=\"cursos-assinatura\">Cursos e Assinaturas<\/h2>\n\n\n\n<p>Prepare-se com o melhor material e com quem mais aprova em Concursos P\u00fablicos em todo o pa\u00eds!<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-cyan-blue-color has-text-color has-background\" style=\"background-color:#0078bd\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-abertos\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">Concursos Abertos<\/mark><\/strong><\/a><\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-cyan-blue-color has-text-color has-background\" style=\"background-color:#0078bd\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-2026\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">Concursos 2026<\/mark><\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aprenda os conceitos essenciais para a resolu\u00e7\u00e3o de quest\u00f5es sobre combina\u00e7\u00e3o com um resumo para as principais provas de concursos. Ol\u00e1, pessoal! Tudo bem com voc\u00eas? A combina\u00e7\u00e3o \u00e9 um dos conceitos centrais da an\u00e1lise combinat\u00f3ria e aparece com frequ\u00eancia em quest\u00f5es que envolvem escolha de elementos sem considerar a ordem. Diferente do arranjo e [&hellip;]<\/p>\n","protected":false},"author":3098,"featured_media":1758240,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[2313,1,3766,220184,220242,214992,220181,1983,220182,220183,222427,1988,222278,220191,222408,1984,220737,214710,222239,222235,222236,222237],"tags":[],"tax_estado":[219964,219965,219966,219967,219968,219969,219963,219970,219971,219972,219973,219974,219975,219976,219977,219978,219979,219980,219981,219982,219983,219984,219985,219986,219987,219988,219989,219990],"class_list":["post-1760218","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-carreiras-bancarias","category-cursos-e-concursos","category-educacional","category-engenharias-e-ti","category-estrategia-militares","category-concursos-administrativos","category-area-financeira","category-fiscal-estadual","category-fiscal-federal","category-fiscal-municipal","category-petrobras","category-policia","category-prefeituras","category-previdenciaria","category-tecnologia-da-informacao","category-tribunais","category-tribunais-tribunais","category-tribunais-de-contas","category-tribunais-regionais-federais","category-tribunal-de-justica","category-tribunal-regional-do-trabalho","category-tribunal-regional-eleitoral","tax_estado-ac","tax_estado-al","tax_estado-am","tax_estado-ap","tax_estado-ba","tax_estado-ce","tax_estado-concursos-federais","tax_estado-df","tax_estado-es","tax_estado-go","tax_estado-ma","tax_estado-mg","tax_estado-ms","tax_estado-mt","tax_estado-pa","tax_estado-pb","tax_estado-pe","tax_estado-pi","tax_estado-pr","tax_estado-rj","tax_estado-rn","tax_estado-ro","tax_estado-rr","tax_estado-rs","tax_estado-sc","tax_estado-se","tax_estado-sp","tax_estado-to"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.2 (Yoast SEO v27.2) - 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