{"id":7230,"date":"2011-12-02T20:10:03","date_gmt":"2011-12-02T20:10:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7230"},"modified":"2022-01-25T23:27:53","modified_gmt":"2022-01-25T23:27:53","slug":"numeros-da-tmn","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7230","title":{"rendered":"N\u00fameros da TMN"},"content":{"rendered":"<p><ul id='GTTabs_ul_7230' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7230' class='GTTabs_curr'><a  id=\"7230_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7230' ><a  id=\"7230_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_7230'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7231\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7231\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN.png\" data-orig-size=\"256,256\" 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=\"TMN\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN.png\" class=\"alignright size-full wp-image-7231\" title=\"TMN\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN.png\" alt=\"\" width=\"92\" height=\"92\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN.png 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/TMN-150x150.png 150w\" sizes=\"auto, (max-width: 92px) 100vw, 92px\" \/><\/a>Como \u00e9 sabido, os n\u00fameros de telem\u00f3vel da operadora TMN t\u00eam 9 algarismos come\u00e7ando sempre por 96.<\/p>\n<p>Quantos desses n\u00fameros s\u00e3o m\u00faltiplos de dez e t\u00eam todos os algarismos deferentes?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7230' onClick='GTTabs_show(1,7230)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7230'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Como se sabe, um n\u00famero \u00e9 m\u00faltiplo de dez quando o algarismo das unidades \u00e9 0.<\/p>\n<p>Os n\u00fameros pretendidos s\u00e3o, portanto, da forma:<\/p>\n<table class=\" aligncenter\" style=\"width: 50%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"border: #00bfff 1px solid;\">9<\/td>\n<td style=\"border: #00bfff 1px solid;\">6<\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>1<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>2<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>3<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>4<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>5<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">x<sub>6<\/sub><\/td>\n<td style=\"border: #00bfff 1px solid;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Os algarismos x<sub>1<\/sub> a\u00a0x<sub>6<\/sub> ser\u00e3o escolhidos, sem repeti\u00e7\u00e3o,\u00a0entre os sete ainda n\u00e3o utilizados: 1, 2, 3, 4, 5, 7 e 8.<\/p>\n<p>Estes 6 algarismos podem ser escolhidos de ${}^{7}{{C}_{6}}=7$ maneiras diferentes. A cada uma destas maneiras correspondem ${{P}_{6}}=6!$ n\u00fameros de telem\u00f3vel de acordo com as condi\u00e7\u00f5es estabelecidas.<\/p>\n<p>Assim, o n\u00famero pedido \u00e9 $N={}^{7}{{C}_{6}}\\times 6!={}^{7}{{A}_{6}}=5040$.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7230' onClick='GTTabs_show(0,7230)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Como \u00e9 sabido, os n\u00fameros de telem\u00f3vel da operadora TMN t\u00eam 9 algarismos come\u00e7ando sempre por 96. Quantos desses n\u00fameros s\u00e3o m\u00faltiplos de dez e t\u00eam todos os algarismos deferentes? Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21051,"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-7230","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":2037,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/12V1Pag177-61_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7230","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=7230"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7230\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21051"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7230"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}