{"id":7187,"date":"2011-11-20T23:14:45","date_gmt":"2011-11-20T23:14:45","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7187"},"modified":"2022-01-25T22:23:03","modified_gmt":"2022-01-25T22:23:03","slug":"num-pelotao-ha-dezasseis-soldados","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7187","title":{"rendered":"Num pelot\u00e3o h\u00e1 dezasseis soldados"},"content":{"rendered":"<p><ul id='GTTabs_ul_7187' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7187' class='GTTabs_curr'><a  id=\"7187_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7187' ><a  id=\"7187_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7187'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7188\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7188\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers.jpg\" data-orig-size=\"550,260\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Soldados\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers.jpg\" class=\"alignright wp-image-7188\" title=\"Soldados\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers.jpg\" alt=\"\" width=\"300\" height=\"142\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers.jpg 550w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers-300x141.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers-150x70.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/four-soldiers-400x189.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Num pelot\u00e3o h\u00e1 dezasseis soldados.<\/p>\n<ol>\n<li>Quantas &#8220;guardas&#8221; diferentes se podem formar, com 4 soldados?<\/li>\n<li>Um dos soldados chama-se Rui. Em quantas dessas &#8220;guardas&#8221; estar\u00e1 o Rui?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7187' onClick='GTTabs_show(1,7187)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7187'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>A &#8220;guarda&#8221; \u00e9 distinta pelos soldados que a constituem, n\u00e3o interessando a ordem destes.<br \/>\nLogo, com 16 soldados podemos constituir ${}^{16}{{C}_{4}}=\\frac{16\\times 15\\times 14\\times 13\\times 12!}{12!\\times 4!}=\\frac{16\\times 15\\times 14\\times 13}{4\\times 3\\times 2\\times 1}=1820$ &#8220;guardas&#8221; diferentes de 4 soldados.<br \/>\n\u00ad<\/li>\n<li>Como o Rui pertence a cada uma dessas &#8220;guardas&#8221;, resta escolher os restantes 3 soldados que constituir\u00e3o a &#8220;guarda&#8221; de entre os 15 soldados dispon\u00edveis. Assim, o Rui estar\u00e1 presente em ${}^{15}{{C}_{3}}=\\frac{15\\times 14\\times 13\\times 12!}{12!\\times 3!}=\\frac{15\\times 14\\times 13}{3\\times 2\\times 1}=455$ dessas &#8220;guardas&#8221;.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7187' onClick='GTTabs_show(0,7187)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num pelot\u00e3o h\u00e1 dezasseis soldados. Quantas &#8220;guardas&#8221; diferentes se podem formar, com 4 soldados? Um dos soldados chama-se Rui. Em quantas dessas &#8220;guardas&#8221; estar\u00e1 o Rui? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":21035,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255],"series":[],"class_list":["post-7187","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-analise-combinatoria"],"views":2447,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag174-44_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7187","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7187"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7187\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21035"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7187"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}