{"id":1760002,"date":"2026-05-21T14:57:00","date_gmt":"2026-05-21T17:57:00","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=1760002"},"modified":"2026-05-19T12:23:46","modified_gmt":"2026-05-19T15:23:46","slug":"arranjo-v2","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/arranjo-v2\/","title":{"rendered":"Arranjo"},"content":{"rendered":"\n<p class=\"has-medium-font-size\">Aprenda os conceitos essenciais para a resolu\u00e7\u00e3o de quest\u00f5es sobre arranjo 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>O <strong>arranjo<\/strong> \u00e9 um dos principais conceitos da <strong>an\u00e1lise combinat\u00f3ria<\/strong> e aparece com frequ\u00eancia em quest\u00f5es que envolvem <strong>sele\u00e7\u00e3o e ordena\u00e7\u00e3o parcial de elementos<\/strong>. Diferente da permuta\u00e7\u00e3o, nem todos os elementos precisam ser utilizados, mas a <strong>ordem continua sendo importante<\/strong>.<\/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 muito comum encontrar situa\u00e7\u00f5es em que o candidato precisa decidir rapidamente entre <strong>arranjo, combina\u00e7\u00e3o ou permuta\u00e7\u00e3o<\/strong>, sendo esse um dos pontos mais cobrados e que mais geram erro.<\/p>\n\n\n\n<p>Neste artigo, voc\u00ea vai entender o conceito de arranjo, suas aplica\u00e7\u00f5es pr\u00e1ticas e como resolver quest\u00f5es com seguran\u00e7a, com exemplos t\u00edpicos 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 arranjo;<\/li>\n\n\n\n<li>Arranjo simples;<\/li>\n\n\n\n<li>Arranjo com repeti\u00e7\u00e3o;<\/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-arranjo\">Arranjo<\/h2>\n\n\n\n<p>Arranjo \u00e9 o processo de <strong>escolher e organizar uma parte dos elementos dispon\u00edveis<\/strong>, levando em considera\u00e7\u00e3o a <strong>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 desses elementos importa.<\/li>\n<\/ul>\n\n\n\n<p><strong>Por exemplo: <\/strong>com os elementos A, B e C, escolhendo 2 por vez, temos as seguintes possibilidades:<\/p>\n\n\n\n<p class=\"has-text-align-center\">AB, BA, AC, CA, BC, CB<\/p>\n\n\n\n<p>Portanto, no total, temos <strong>6 possibilidades<\/strong>.<\/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>O arranjo aparece em diversas situa\u00e7\u00f5es pr\u00e1ticas, como por exemplo:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Forma\u00e7\u00e3o de senhas;<\/li>\n\n\n\n<li>Organiza\u00e7\u00e3o de posi\u00e7\u00f5es (1\u00ba, 2\u00ba, 3\u00ba lugar);<\/li>\n\n\n\n<li>C\u00f3digos e placas;<\/li>\n\n\n\n<li>Distribui\u00e7\u00e3o de cargos diferentes.<\/li>\n<\/ul>\n\n\n\n<p><strong><em>Dica<\/em><\/strong><strong>:<\/strong> sempre que houver <strong>ordem + escolha parcial<\/strong>, pense em arranjo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-arranjo-simples\">Arranjo Simples<\/h2>\n\n\n\n<p>O arranjo simples ocorre quando <strong>n\u00e3o h\u00e1 repeti\u00e7\u00e3o de elementos<\/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=\"133\" height=\"57\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05114422\/image-29.png\" alt=\"F\u00f3rmula do arranjo simples\" class=\"wp-image-1760003\"\/><\/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>Quantos grupos diferentes de 2 pessoas podem ser formados em uma sala com 5 pessoas?<\/p>\n\n\n\n<p>Resolu\u00e7\u00e3o:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"59\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05114441\/image-30.png\" alt=\"Exemplo resolvido - arranjo simples\" class=\"wp-image-1760004\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05114441\/image-30.png 357w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05114441\/image-30-300x50.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05114441\/image-30-150x25.png 150w\" sizes=\"auto, (max-width: 357px) 100vw, 357px\" \/><\/figure>\n\n\n\n<p>Portanto, podemos formar <strong>20 grupos<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-arranjo-com-repeticao\">Arranjo com repeti\u00e7\u00e3o<\/h2>\n\n\n\n<p>Por outro lado, o arranjo com repeti\u00e7\u00e3o ocorre quando <strong>os elementos podem se repetir<\/strong>.<\/p>\n\n\n\n<p><strong>F\u00f3rmula<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>AR<sub>n,p<\/sub> = n<sup>p<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Exemplo<\/strong><\/p>\n\n\n\n<p>Quantas senhas de 3 d\u00edgitos podem ser formadas usando os n\u00fameros de 0 a 9?<\/p>\n\n\n\n<p>Resolu\u00e7\u00e3o:<\/p>\n\n\n\n<p>Devemos escolher 3 n\u00fameros entre 10 dispon\u00edveis, sendo que pode haver repeti\u00e7\u00e3o. Assim:<\/p>\n\n\n\n<p class=\"has-text-align-center\">AR<sub>10,3<\/sub> = 10 \u00d7 10 \u00d7 10 = 10\u00b3 = 1.000<\/p>\n\n\n\n<p>Portanto, podemos formar <strong>1.000 senhas<\/strong> de 3 d\u00edgitos nessas condi\u00e7\u00f5es.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-exemplos-resolvidos-arranjo\">Exemplos Resolvidos &#8211; Arranjo<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-1\"><strong>Exemplo 1<\/strong><\/h3>\n\n\n\n<p>Uma competi\u00e7\u00e3o possui 6 participantes. De quantas formas podemos definir o p\u00f3dio (1\u00ba, 2\u00ba e 3\u00ba lugar)?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p>A ordem importa, pois cada posi\u00e7\u00e3o \u00e9 diferente. Logo:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"261\" height=\"61\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05121052\/image-31.png\" alt=\"Exemplo 1 resolvido\" class=\"wp-image-1760005\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05121052\/image-31.png 261w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/05\/05121052\/image-31-150x35.png 150w\" sizes=\"auto, (max-width: 261px) 100vw, 261px\" \/><\/figure>\n\n\n\n<p>Portanto, <strong>120 formas<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-2\"><strong>Exemplo 2<\/strong><\/h3>\n\n\n\n<p>Quantas placas com 2 letras podem ser formadas usando o alfabeto (26 letras), permitindo repeti\u00e7\u00e3o?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p>Como h\u00e1 repeti\u00e7\u00e3o, utilizamos pot\u00eancia. Logo:<\/p>\n\n\n\n<p class=\"has-text-align-center\">AR<sub>26,2<\/sub> = 26\u00b2 = 676<\/p>\n\n\n\n<p>Portanto, <strong>676 placas<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-exemplo-3\"><strong>Exemplo 3<\/strong><\/h3>\n\n\n\n<p>Quantas senhas de 3 caracteres podem ser formadas com letras A, B, C, sendo que a primeira n\u00e3o pode se repetir nas demais posi\u00e7\u00f5es?<\/p>\n\n\n\n<p><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Primeira posi\u00e7\u00e3o: 3 op\u00e7\u00f5es<\/li>\n\n\n\n<li>Segunda posi\u00e7\u00e3o: 2 op\u00e7\u00f5es<\/li>\n\n\n\n<li>Terceira posi\u00e7\u00e3o: 2 op\u00e7\u00f5es<\/li>\n<\/ul>\n\n\n\n<p>Total:<\/p>\n\n\n\n<p class=\"has-text-align-center\">3 \u00d7 2 \u00d7 2 = 12<\/p>\n\n\n\n<p>Ou seja, <strong>12 senhas<\/strong>. <\/p>\n\n\n\n<p>Nesse caso, a quest\u00e3o exige interpreta\u00e7\u00e3o e restri\u00e7\u00e3o, n\u00e3o apenas aplica\u00e7\u00e3o direta de f\u00f3rmula. Por isso \u00e9 importante entender o que o enunciado est\u00e1 pedindo, e n\u00e3o apenas decorar f\u00f3rmulas.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\" id=\"h-resumo-arranjo\">Resumo \u2013 Arranjo<\/h2>\n\n\n\n<p>Para te ajudar a revisar os principais pontos que vimos at\u00e9 aqui sobre arranjo, 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 arranjo<\/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\">Arranjo simples<\/td><td class=\"has-text-align-center\" data-align=\"center\">Sem repeti\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">n!\/(n-p)!<\/td><td class=\"has-text-align-center\" data-align=\"center\">ordem importa, posi\u00e7\u00f5es, ranking<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Arranjo com repeti\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">Com repeti\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">n<sup>p<\/sup><\/td><td class=\"has-text-align-center\" data-align=\"center\">senha, c\u00f3digo, repeti\u00e7\u00e3o permitida<\/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-arranjo\">Finalizando &#8211; Arranjo<\/h2>\n\n\n\n<p>O arranjo \u00e9 uma ferramenta essencial para resolver problemas em que precisamos escolher e ordenar elementos simultaneamente. O ponto central est\u00e1 em identificar se a ordem influencia o resultado e se h\u00e1 repeti\u00e7\u00e3o permitida.<\/p>\n\n\n\n<p>Muitos erros em prova n\u00e3o acontecem por falta de conhecimento da f\u00f3rmula, mas por falha na interpreta\u00e7\u00e3o do enunciado. Por isso, desenvolver o h\u00e1bito de analisar cuidadosamente o problema antes de aplicar qualquer c\u00e1lculo \u00e9 fundamental. Com <strong>pr\u00e1tica<\/strong>, o reconhecimento desses padr\u00f5es se torna autom\u00e1tico, permitindo resolver quest\u00f5es com mais rapidez e precis\u00e3o, consolidando o desempenho em an\u00e1lise combinat\u00f3ria.<\/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 de arranjo 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 arranjo com um resumo para as principais provas de concursos. Ol\u00e1, pessoal! Tudo bem com voc\u00eas? O arranjo \u00e9 um dos principais conceitos da an\u00e1lise combinat\u00f3ria e aparece com frequ\u00eancia em quest\u00f5es que envolvem sele\u00e7\u00e3o e ordena\u00e7\u00e3o parcial de elementos. Diferente da permuta\u00e7\u00e3o, nem todos [&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],"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-1760002","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","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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