Quiz — cours_denomb.pdf

Question 1 sur 10 20:00

[{"id":7785,"question":"Combien de permutations peut-on former avec les lettres du mot 'MATH' ?","option_a":"12","option_b":"24","option_c":"48","option_d":"6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le nombre de permutations de n éléments distincts est n!. Pour 'MATH', n=4, donc 4! = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12\", \"b\": \"24\", \"c\": \"48\", \"d\": \"6\"}}","_debug_options_count":4},{"id":7786,"question":"Un arrangement de 3 éléments parmi 5 est-il différent d'une permutation de 3 éléments parmi 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un arrangement tient compte de l'ordre, tout comme une permutation. Les deux termes sont souvent utilisés de manière interchangeable dans ce contexte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7787,"question":"Combien de combinaisons de 2 éléments peut-on former à partir de l'ensemble {A, B, C, D} ?","option_a":"6","option_b":"12","option_c":"4","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le nombre de combinaisons de k éléments parmi n est donné par C(n,k) = n! \/ (k!(n-k)!). Ici, C(4,2) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6\", \"b\": \"12\", \"c\": \"4\", \"d\": \"8\"}}","_debug_options_count":4},{"id":7788,"question":"Si on tire 3 cartes d'un jeu de 52 cartes, l'ordre de tirage est-il important pour calculer le nombre de mains possibles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans une main de cartes, l'ordre n'est pas important. On utilise donc une combinaison, pas une permutation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7789,"question":"Quel est le nombre d'arrangements de 2 éléments parmi 4 ?","option_a":"6","option_b":"12","option_c":"8","option_d":"4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le nombre d'arrangements de k éléments parmi n est A(n,k) = n! \/ (n-k)!. Ici, A(4,2) = 4! \/ 2! = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"6\", \"b\": \"12\", \"c\": \"8\", \"d\": \"4\"}}","_debug_options_count":4},{"id":7790,"question":"La formule C(n,k) = C(n, n-k) est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car choisir k éléments parmi n revient à en laisser n-k de côté. La formule est donc symétrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7791,"question":"Combien de façons peut-on choisir 1 président et 1 vice-président parmi 10 personnes ?","option_a":"10","option_b":"45","option_c":"90","option_d":"100","option_e":"","option_f":"","bonne_reponse":"c","explication":"Cela revient à un arrangement de 2 éléments parmi 10 (A(10,2) = 10 × 9 = 90).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"10\", \"b\": \"45\", \"c\": \"90\", \"d\": \"100\"}}","_debug_options_count":4},{"id":7792,"question":"Le dénombrement est-il utile en probabilités ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car il permet de calculer le nombre de cas favorables ou possibles dans une expérience aléatoire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7793,"question":"Quel est le nombre de permutations de l'ensemble {1, 2, 3, 4, 5} ?","option_a":"20","option_b":"60","option_c":"120","option_d":"24","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le nombre de permutations de n éléments est n!. Ici, 5! = 120.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"20\", \"b\": \"60\", \"c\": \"120\", \"d\": \"24\"}}","_debug_options_count":4},{"id":7794,"question":"Peut-on utiliser le dénombrement pour résoudre des problèmes de géométrie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, par exemple pour compter le nombre de triangles formés par des points dans un plan.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]