{"id":1560,"date":"2026-09-08T08:07:49","date_gmt":"2026-09-08T08:07:49","guid":{"rendered":"https:\/\/maroczain.com\/scolaire.maroczain.com\/?page_id=1560"},"modified":"2026-09-08T08:07:49","modified_gmt":"2026-09-08T08:07:49","slug":"compter-organiser-choisir","status":"publish","type":"page","link":"https:\/\/maroczain.com\/scolaire.maroczain.com\/compter-organiser-choisir\/","title":{"rendered":"Compter. Organiser. Choisir"},"content":{"rendered":"\n&#8220;`html\n<div id=\"mza-denombrement-cpge\">\n\n<style>\n#mza-denombrement-cpge,\n#mza-denombrement-cpge *{box-sizing:border-box}\n\n#mza-denombrement-cpge{\n --navy:#06172c;\n --navy2:#0d416d;\n --gold:#c99a36;\n --gold2:#efd68c;\n --paper:#f5f6f8;\n --white:#fff;\n --text:#18283a;\n --muted:#687789;\n --line:#dfe5eb;\n font-family:Arial,Helvetica,sans-serif;\n background:var(--paper);\n color:var(--text);\n overflow:hidden\n}\n\n#mza-denombrement-cpge a{text-decoration:none;color:inherit}\n#mza-denombrement-cpge .wrap{max-width:1200px;margin:auto;padding:0 24px}\n#mza-denombrement-cpge section{padding:68px 0}\n\n#mza-denombrement-cpge .hero{\n color:#fff;\n padding:72px 0;\n background:\n radial-gradient(circle at 84% 15%,rgba(213,169,68,.28),transparent 28%),\n linear-gradient(135deg,#041224,#082b4c 65%,#10517e)\n}\n\n#mza-denombrement-cpge .badge{\n display:inline-block;\n padding:8px 13px;\n border-radius:999px;\n border:1px solid 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border-radius:14px;\n background:var(--navy);\n color:#fff\n}\n\n#mza-denombrement-cpge .cta{\n text-align:center;\n padding:50px 24px;\n border-radius:25px;\n background:linear-gradient(135deg,#06172c,#0d416d);\n color:#fff\n}\n\n#mza-denombrement-cpge .cta h2{color:#fff}\n\n#mza-denombrement-cpge .cta p{\n max-width:760px;\n margin:0 auto 22px;\n color:#cfdae4;\n line-height:1.7\n}\n\n@media(max-width:900px){\n #mza-denombrement-cpge .grid,\n #mza-denombrement-cpge .method{\n   grid-template-columns:1fr\n }\n}\n<\/style>\n\n<header class=\"hero\">\n<div class=\"wrap\">\n\n<span class=\"badge\">COURS 16 \u2022 D\u00c9NOMBREMENT &#038; COMBINATOIRE<\/span>\n\n<h1>Compter.<br>Organiser. Choisir.<\/h1>\n\n<p class=\"lead\">\nLe d\u00e9nombrement consiste \u00e0 compter efficacement sans \u00e9num\u00e9rer.\nEn CPGE, il faut savoir reconna\u00eetre imm\u00e9diatement si l&#8217;ordre compte,\nsi les r\u00e9p\u00e9titions sont autoris\u00e9es et si l&#8217;on effectue un choix,\nun arrangement ou une permutation.\n<\/p>\n\n<div class=\"actions\">\n<a href=\"#cours\" class=\"btn gold\">\ud83d\udcda COMMENCER<\/a>\n<a href=\"#methode\" class=\"btn glass\">\ud83e\udde0 M\u00c9THODE<\/a>\n<a href=\"#exercices\" class=\"btn glass\">\ud83e\udde9 EXERCICES<\/a>\n<a href=\"#qcm\" class=\"btn glass\">\u2753 QCM<\/a>\n<\/div>\n\n<\/div>\n<\/header>\n\n<section id=\"cours\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">1. PRINCIPE ADDITIF<\/span>\n<h2>Additionner les possibilit\u00e9s exclusives.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Principe<\/h3>\n<p>\nSi une situation peut se produire selon plusieurs cas incompatibles,\non additionne les nombres de possibilit\u00e9s.\n<\/p>\n\n<div class=\"formula\">\nN = N\u2081 + N\u2082 + &#8230; + N\u2096\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n<p>\nUn \u00e9l\u00e8ve choisit soit un livre de math\u00e9matiques parmi 5,\nsoit un livre de physique parmi 4.\n<\/p>\n\n<div class=\"formula\">\n5 + 4 possibilit\u00e9s\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">2. PRINCIPE MULTIPLICATIF<\/span>\n<h2>Multiplier les choix successifs.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Principe<\/h3>\n\n<p>\nSi une proc\u00e9dure comporte plusieurs \u00e9tapes successives ind\u00e9pendantes,\non multiplie le nombre de possibilit\u00e9s de chaque \u00e9tape.\n<\/p>\n\n<div class=\"formula\">\nN = N\u2081 \u00d7 N\u2082 \u00d7 &#8230; \u00d7 N\u2096\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n\n<p>\n3 chemises et 4 pantalons donnent :\n<\/p>\n\n<div class=\"formula\">\n3 \u00d7 4 = 12 tenues\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">3. FACTORIELLE<\/span>\n<h2>Le moteur des permutations.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>D\u00e9finition<\/h3>\n\n<div class=\"formula\">\nn! = n(n-1)(n-2)&#8230;2\u00d71\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Convention<\/h3>\n\n<div class=\"formula\">\n0! = 1\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n\n<div class=\"formula\">\n5! = 5\u00d74\u00d73\u00d72\u00d71\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Usage<\/h3>\n\n<p>\nLa factorielle appara\u00eet lorsque l&#8217;on ordonne tous les \u00e9l\u00e9ments d&#8217;un ensemble.\n<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section id=\"methode\" class=\"dark\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\" style=\"color:#efd68c\">MZA COUNTING ENGINE<\/span>\n<h2>Six questions avant tout calcul.<\/h2>\n<\/div>\n\n<div class=\"method\">\n<div><b>01<\/b><span>COMBIEN D&#8217;\u00c9L\u00c9MENTS ?<\/span><\/div>\n<div><b>02<\/b><span>COMBIEN CHOISIS ?<\/span><\/div>\n<div><b>03<\/b><span>ORDRE ?<\/span><\/div>\n<div><b>04<\/b><span>R\u00c9P\u00c9TITION ?<\/span><\/div>\n<div><b>05<\/b><span>CAS EXCLUSIFS ?<\/span><\/div>\n<div><b>06<\/b><span>FORMULE<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">4. PERMUTATIONS<\/span>\n<h2>Ordonner tous les \u00e9l\u00e9ments.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Sans r\u00e9p\u00e9tition<\/h3>\n\n<p>\nLe nombre de permutations de n \u00e9l\u00e9ments distincts est :\n<\/p>\n\n<div class=\"formula\">\nP\u2099 = n!\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n\n<p>\nLe nombre d&#8217;ordres possibles de 6 candidats est :\n<\/p>\n\n<div class=\"formula\">\n6!\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Avec r\u00e9p\u00e9titions<\/h3>\n\n<p>\nSi certains \u00e9l\u00e9ments sont identiques :\n<\/p>\n\n<div class=\"formula\">\nn! \/ (n\u2081!n\u2082!&#8230;n\u2096!)\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple classique<\/h3>\n\n<p>\nPour les lettres d&#8217;un mot comportant plusieurs lettres identiques,\nil faut corriger les permutations compt\u00e9es plusieurs fois.\n<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">5. ARRANGEMENTS<\/span>\n<h2>Choisir puis ordonner.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>D\u00e9finition<\/h3>\n\n<p>\nOn choisit p \u00e9l\u00e9ments parmi n et l&#8217;ordre compte.\n<\/p>\n\n<div class=\"formula\">\nA\u2099\u1d56 = n! \/ (n-p)!\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n\n<p>\nFormer un podium de 3 personnes parmi 10 candidats :\n<\/p>\n\n<div class=\"formula\">\nA\u2081\u2080\u00b3\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>R\u00e9flexe<\/h3>\n\n<p>\nPremier, deuxi\u00e8me et troisi\u00e8me sont des positions diff\u00e9rentes :\nl&#8217;ordre compte donc.\n<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Cas p=n<\/h3>\n\n<div class=\"formula\">\nA\u2099\u207f = n!\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">6. COMBINAISONS<\/span>\n<h2>Choisir sans tenir compte de l&#8217;ordre.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>D\u00e9finition<\/h3>\n\n<div class=\"formula\">\nC(n,p) = n! \/ [p!(n-p)!]\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Notation<\/h3>\n\n<div class=\"formula\">\nC(n,p) = (n parmi p)\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple<\/h3>\n\n<p>\nChoisir 4 \u00e9tudiants parmi 12 :\n<\/p>\n\n<div class=\"formula\">\nC(12,4)\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Sym\u00e9trie<\/h3>\n\n<div class=\"formula\">\nC(n,p)=C(n,n-p)\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">7. IDENTIT\u00c9S BINOMIALES<\/span>\n<h2>Manipuler les coefficients binomiaux.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Pascal<\/h3>\n\n<div class=\"formula\">\nC(n,p)=C(n-1,p)+C(n-1,p-1)\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Somme d&#8217;une ligne<\/h3>\n\n<div class=\"formula\">\n\u03a3 C(n,p)=2\u207f\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Extr\u00e9mit\u00e9s<\/h3>\n\n<div class=\"formula\">\nC(n,0)=C(n,n)=1\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Relation utile<\/h3>\n\n<div class=\"formula\">\npC(n,p)=nC(n-1,p-1)\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">8. BIN\u00d4ME DE NEWTON<\/span>\n<h2>D\u00e9velopper une puissance efficacement.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\n(a+b)\u207f = \u03a3 C(n,k)a\u207f\u207b\u1d4fb\u1d4f\n<\/div>\n\n<p>\nLa somme porte sur k allant de 0 \u00e0 n.\n<\/p>\n\n<\/div>\n\n<div class=\"tip\">\nLes coefficients du d\u00e9veloppement sont pr\u00e9cis\u00e9ment les coefficients binomiaux.\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">9. AVEC OU SANS R\u00c9P\u00c9TITION<\/span>\n<h2>Le pi\u00e8ge classique des concours.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Sans r\u00e9p\u00e9tition<\/h3>\n\n<p>\nUn \u00e9l\u00e9ment d\u00e9j\u00e0 choisi ne peut plus \u00eatre repris.\n<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Avec r\u00e9p\u00e9tition<\/h3>\n\n<p>\nUn m\u00eame \u00e9l\u00e9ment peut \u00eatre choisi plusieurs fois.\n<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Exemple code PIN<\/h3>\n\n<p>\nPour un code de 4 chiffres avec r\u00e9p\u00e9tition autoris\u00e9e :\n<\/p>\n\n<div class=\"formula\">\n10\u2074\n<\/div>\n<\/div>\n\n<div class=\"card\">\n<h3>Sans r\u00e9p\u00e9tition<\/h3>\n\n<p>\nSi les quatre chiffres doivent \u00eatre distincts :\n<\/p>\n\n<div class=\"formula\">\n10\u00d79\u00d78\u00d77\n<\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">10. COMPL\u00c9MENTAIRE<\/span>\n<h2>Compter ce que l&#8217;on ne veut pas.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nPour compter des objets satisfaisant une condition difficile,\nil est parfois plus simple de compter le total puis de retirer les cas interdits.\n<\/p>\n\n<div class=\"formula\">\nN(favorable)=N(total)-N(interdit)\n<\/div>\n\n<\/div>\n\n<div class=\"tip\">\nTr\u00e8s utile pour les expressions \u00ab au moins un \u00bb, \u00ab aucun \u00bb, \u00ab pas tous \u00bb, \u00ab au moins deux \u00bb.\n<\/div>\n\n<\/div>\n<\/section>\n\n<section id=\"exercices\" style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">11. EXERCICES PROGRESSIFS<\/span>\n<h2>Reconna\u00eetre la bonne structure.<\/h2>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 1<\/span>\n\n<h3>Exercice 1 \u2014 Permutations<\/h3>\n\n<p>\nDe combien de fa\u00e7ons peut-on ranger 7 livres distincts sur une \u00e9tag\u00e8re ?\n<\/p>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenHint('denHint1')\">\ud83d\udca1 INDICE<\/button>\n\n<div id=\"denHint1\" class=\"hint\">\nTous les livres sont utilis\u00e9s et l&#8217;ordre compte.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 2<\/span>\n\n<h3>Exercice 2 \u2014 Combinaison<\/h3>\n\n<p>\nUne classe compte 20 \u00e9l\u00e8ves. Combien peut-on former de groupes de 4 \u00e9l\u00e8ves ?\n<\/p>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenHint('denHint2')\">\ud83d\udca1 INDICE<\/button>\n\n<div id=\"denHint2\" class=\"hint\">\nDans un groupe de 4, changer l&#8217;ordre des \u00e9l\u00e8ves ne cr\u00e9e pas un nouveau groupe.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 3<\/span>\n\n<h3>Exercice 3 \u2014 Arrangement<\/h3>\n\n<p>\nParmi 12 coureurs, combien de podiums distincts peut-on obtenir ?\n<\/p>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenHint('denHint3')\">\ud83d\udca1 INDICE<\/button>\n\n<div id=\"denHint3\" class=\"hint\">\nTrois coureurs sont choisis, mais les positions 1, 2 et 3 sont diff\u00e9rentes.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU PR\u00c9PA<\/span>\n\n<h3>Exercice 4 \u2014 Contrainte<\/h3>\n\n<p>\nCombien de mots de 6 lettres peut-on former avec 6 lettres distinctes\nsi deux lettres donn\u00e9es doivent rester c\u00f4te \u00e0 c\u00f4te ?\n<\/p>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenHint('denHint4')\">\ud83d\udca1 INDICE<\/button>\n\n<div id=\"denHint4\" class=\"hint\">\nRegroupez d&#8217;abord les deux lettres impos\u00e9es comme un seul bloc, puis pensez \u00e0 leur ordre interne.\n<\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">12. PROBLEM LAB<\/span>\n<h2>Mission : comit\u00e9 avec contraintes.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<h3>Mission CPGE<\/h3>\n\n<p>\nUne association compte 8 femmes et 7 hommes.\nOn souhaite former un comit\u00e9 de 5 personnes.\n<\/p>\n\n<p>\u00c9tudier successivement le nombre de comit\u00e9s :<\/p>\n\n<ol>\n<li>sans aucune contrainte ;<\/li>\n<li>comportant exactement 3 femmes ;<\/li>\n<li>comportant au moins une femme ;<\/li>\n<li>comportant au moins 2 hommes ;<\/li>\n<li>dans lequel deux personnes donn\u00e9es ne peuvent pas si\u00e9ger ensemble ;<\/li>\n<li>dans lequel une personne donn\u00e9e doit obligatoirement \u00eatre pr\u00e9sente.<\/li>\n<\/ol>\n\n<div class=\"actions\">\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenHint('denMission1')\">\ud83d\udca1 INDICE<\/button>\n<button type=\"button\" class=\"btn\" style=\"background:#06172c;color:#fff\" onclick=\"mzaDenHint('denMission2')\">\ud83e\udde0 M\u00c9THODE<\/button>\n<\/div>\n\n<div id=\"denMission1\" class=\"hint\">\nPour \u00ab au moins une femme \u00bb, utilisez le compl\u00e9mentaire : total moins comit\u00e9s compos\u00e9s uniquement d&#8217;hommes.\n<\/div>\n\n<div id=\"denMission2\" class=\"hint\">\nPour chaque question, identifiez d&#8217;abord si l&#8217;ordre compte. Ici, un comit\u00e9 est un ensemble de personnes : l&#8217;ordre ne compte pas.\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"dark\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\" style=\"color:#efd68c\">MZA COMBINATORICS LAB<\/span>\n<h2>Ne choisissez pas une formule avant d&#8217;avoir compris la situation.<\/h2>\n\n<p>\nLa majorit\u00e9 des erreurs de d\u00e9nombrement viennent d&#8217;un mauvais diagnostic :\nordre, r\u00e9p\u00e9tition, exclusion ou compl\u00e9mentaire.\n<\/p>\n<\/div>\n\n<div class=\"method\">\n<div><b>A<\/b><span>ORDRE ?<\/span><\/div>\n<div><b>B<\/b><span>R\u00c9P\u00c9TITION ?<\/span><\/div>\n<div><b>C<\/b><span>TOUT OU PARTIE ?<\/span><\/div>\n<div><b>D<\/b><span>CONTRAINTE ?<\/span><\/div>\n<div><b>E<\/b><span>COMPL\u00c9MENT ?<\/span><\/div>\n<div><b>F<\/b><span>V\u00c9RIFIER<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section id=\"qcm\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">13. QCM DE VALIDATION<\/span>\n<h2>Diagnostic D\u00e9nombrement CPGE.<\/h2>\n\n<p>Le score est affich\u00e9 sans r\u00e9v\u00e9ler les r\u00e9ponses correctes.<\/p>\n<\/div>\n\n<div class=\"qcm\">\n\n<form id=\"denQuiz\">\n\n<div class=\"question\">\n<strong>1. Le nombre de permutations de n objets distincts est :<\/strong>\n<label><input type=\"radio\" name=\"c1\" value=\"1\"> n!<\/label>\n<label><input type=\"radio\" name=\"c1\" value=\"0\"> n\u00b2<\/label>\n<label><input type=\"radio\" name=\"c1\" value=\"0\"> 2n<\/label>\n<label><input type=\"radio\" name=\"c1\" value=\"0\"> n+1<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>2. Choisir p \u00e9l\u00e9ments parmi n sans tenir compte de l&#8217;ordre correspond \u00e0 :<\/strong>\n<label><input type=\"radio\" name=\"c2\" value=\"1\"> une combinaison<\/label>\n<label><input type=\"radio\" name=\"c2\" value=\"0\"> une permutation<\/label>\n<label><input type=\"radio\" name=\"c2\" value=\"0\"> une d\u00e9rivation<\/label>\n<label><input type=\"radio\" name=\"c2\" value=\"0\"> une matrice<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>3. Dans un podium de 3 personnes :<\/strong>\n<label><input type=\"radio\" name=\"c3\" value=\"1\"> l&#8217;ordre compte<\/label>\n<label><input type=\"radio\" name=\"c3\" value=\"0\"> l&#8217;ordre ne compte pas<\/label>\n<label><input type=\"radio\" name=\"c3\" value=\"0\"> toutes les personnes sont identiques<\/label>\n<label><input type=\"radio\" name=\"c3\" value=\"0\"> il n&#8217;y a qu&#8217;une possibilit\u00e9<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>4. La formule C(n,p)=C(n,n-p) exprime :<\/strong>\n<label><input type=\"radio\" name=\"c4\" value=\"1\"> la sym\u00e9trie des coefficients binomiaux<\/label>\n<label><input type=\"radio\" name=\"c4\" value=\"0\"> l&#8217;inversibilit\u00e9 d&#8217;une matrice<\/label>\n<label><input type=\"radio\" name=\"c4\" value=\"0\"> la d\u00e9riv\u00e9e d&#8217;une fonction<\/label>\n<label><input type=\"radio\" name=\"c4\" value=\"0\"> un produit scalaire<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>5. Pour compter \u00ab au moins un \u00bb \u00e9v\u00e9nement favorable, il est souvent utile de :<\/strong>\n<label><input type=\"radio\" name=\"c5\" value=\"1\"> utiliser le compl\u00e9mentaire<\/label>\n<label><input type=\"radio\" name=\"c5\" value=\"0\"> multiplier toujours par n!<\/label>\n<label><input type=\"radio\" name=\"c5\" value=\"0\"> supprimer les contraintes<\/label>\n<label><input type=\"radio\" name=\"c5\" value=\"0\"> utiliser une matrice identit\u00e9<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>6. Le principe multiplicatif s&#8217;applique lorsque :<\/strong>\n<label><input type=\"radio\" name=\"c6\" value=\"1\"> une proc\u00e9dure comporte plusieurs choix successifs<\/label>\n<label><input type=\"radio\" name=\"c6\" value=\"0\"> les cas sont forc\u00e9ment incompatibles<\/label>\n<label><input type=\"radio\" name=\"c6\" value=\"0\"> il n&#8217;existe qu&#8217;un seul choix<\/label>\n<label><input type=\"radio\" name=\"c6\" value=\"0\"> on cherche toujours une combinaison<\/label>\n<\/div>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaDenScore()\">\nVALIDER MON QCM\n<\/button>\n\n<\/form>\n\n<div id=\"denResult\"><\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"cta\">\n\n<div style=\"font-size:43px\">C(n,p)<\/div>\n\n<h2>Le bon d\u00e9nombrement commence avant le calcul.<\/h2>\n\n<p>\nIdentifier si l&#8217;ordre compte, si les r\u00e9p\u00e9titions sont autoris\u00e9es\net si les cas doivent \u00eatre additionn\u00e9s ou multipli\u00e9s\npermet de r\u00e9soudre rapidement une grande partie des probl\u00e8mes de combinatoire.\n<\/p>\n\n<div class=\"actions\" style=\"justify-content:center\">\n<a href=\"#cours\" class=\"btn gold\">\ud83d\udcda REVOIR LE COURS<\/a>\n<a href=\"#exercices\" class=\"btn glass\">\ud83e\udde9 EXERCICES<\/a>\n<a href=\"#qcm\" class=\"btn glass\">\u2753 REFAIRE LE QCM<\/a>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<script>\nfunction mzaDenHint(id){\n const el=document.getElementById(id);\n if(!el)return;\n el.style.display = el.style.display===\"block\" ? \"none\" : \"block\";\n}\n\nfunction mzaDenScore(){\n const form=document.getElementById(\"denQuiz\");\n const result=document.getElementById(\"denResult\");\n\n let score=0;\n let complete=true;\n\n [\"c1\",\"c2\",\"c3\",\"c4\",\"c5\",\"c6\"].forEach(function(name){\n   const answer=form.querySelector('input[name=\"'+name+'\"]:checked');\n\n   if(!answer){\n     complete=false;\n   }else{\n     score+=Number(answer.value);\n   }\n });\n\n result.style.display=\"block\";\n\n if(!complete){\n   result.innerHTML=\"<strong>R\u00e9pondez aux 6 questions avant de valider.<\/strong>\";\n   return;\n }\n\n const pct=Math.round(score\/6*100);\n\n let level=\"D\u00e9nombrement \u00e0 consolider\";\n if(pct>=50) level=\"Bases acquises\";\n if(pct>=67) level=\"Bon niveau\";\n if(pct>=84) level=\"Tr\u00e8s bonne ma\u00eetrise\";\n if(pct===100) level=\"Excellent niveau CPGE\";\n\n result.innerHTML=\n \"<strong style='font-size:30px;color:#efd68c'>\"+pct+\"%<\/strong>\"+\n \"<p><b>\"+level+\"<\/b><\/p>\"+\n \"<p>Score : \"+score+\" \/ 6<\/p>\"+\n \"<p>Les r\u00e9ponses correctes et la correction d\u00e9taill\u00e9e restent masqu\u00e9es.<\/p>\";\n}\n<\/script>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>&#8220;`html COURS 16 \u2022 D\u00c9NOMBREMENT &#038; COMBINATOIRE Compter.Organiser. Choisir. Le d\u00e9nombrement consiste \u00e0 compter efficacement sans \u00e9num\u00e9rer. En CPGE, il faut savoir reconna\u00eetre imm\u00e9diatement si l&#8217;ordre compte, si les r\u00e9p\u00e9titions sont autoris\u00e9es et si l&#8217;on effectue un choix, un arrangement ou une permutation. \ud83d\udcda COMMENCER \ud83e\udde0 M\u00c9THODE \ud83e\udde9 EXERCICES \u2753 QCM 1. PRINCIPE ADDITIF Additionner [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1560","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1560","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/comments?post=1560"}],"version-history":[{"count":1,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1560\/revisions"}],"predecessor-version":[{"id":1562,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1560\/revisions\/1562"}],"wp:attachment":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/media?parent=1560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}