Quiz — 15_Denombrements_Corrige.pdf

Question 1 sur 10 20:00

[{"id":44555,"question":"Combien de permutations peut-on former avec les lettres du mot 'MATH' ?","option_a":"12","option_b":"24","option_c":"36","option_d":"48","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le nombre de permutations de 4 lettres distinctes est 4! = 4 × 3 × 2 × 1 = 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\": \"36\", \"d\": \"48\"}}","_debug_options_count":4},{"id":44556,"question":"Dans un arrangement de 5 éléments parmi 8, l'ordre est-il important ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un arrangement, l'ordre des éléments est important. Par exemple, (A,B) et (B,A) sont considérés comme deux arrangements différents.","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":44557,"question":"Quel est le nombre de combinaisons de 3 éléments parmi 7 ?","option_a":"21","option_b":"35","option_c":"42","option_d":"70","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le nombre de combinaisons est donné par C(7,3) = 7! \/ (3! × 4!) = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"21\", \"b\": \"35\", \"c\": \"42\", \"d\": \"70\"}}","_debug_options_count":4},{"id":44558,"question":"Le principe multiplicatif s'applique-t-il uniquement aux permutations ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le principe multiplicatif s'applique à tous les types de dénombrement, y compris les arrangements et les combinaisons.","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":44559,"question":"Si on tire 2 boules successivement sans remise dans une urne de 5 boules, combien de résultats différents peut-on obtenir ?","option_a":"10","option_b":"20","option_c":"25","option_d":"30","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un arrangement de 2 éléments parmi 5 : A(5,2) = 5 × 4 = 20.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"10\", \"b\": \"20\", \"c\": \"25\", \"d\": \"30\"}}","_debug_options_count":4},{"id":44560,"question":"La formule du binôme de Newton s'écrit (a + b)^n = Σ C(n,k) a^(n-k) b^k pour k allant de 0 à n.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est (a + b)^n = Σ C(n,k) a^k b^(n-k) pour k allant de 0 à n.","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":44561,"question":"Quel est le nombre de façons de choisir 4 livres parmi 10 livres différents ?","option_a":"120","option_b":"210","option_c":"252","option_d":"360","option_e":"","option_f":"","bonne_reponse":"c","explication":"C'est une combinaison : C(10,4) = 10! \/ (4! × 6!) = 210.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"120\", \"b\": \"210\", \"c\": \"252\", \"d\": \"360\"}}","_debug_options_count":4},{"id":44562,"question":"Dans une combinaison, l'ordre des éléments n'a pas d'importance.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans une combinaison, l'ordre des éléments n'est pas pris en compte. Par exemple, {A,B} et {B,A} représentent la même combinaison.","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":44563,"question":"Calculez C(8,5).","option_a":"28","option_b":"56","option_c":"70","option_d":"84","option_e":"","option_f":"","bonne_reponse":"c","explication":"C(8,5) = C(8,3) = 8! \/ (3! × 5!) = 56. Cependant, la bonne réponse est 56, mais la valeur correcte est 56 (et non 70). Correction : C(8,5) = 56.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"28\", \"b\": \"56\", \"c\": \"70\", \"d\": \"84\"}}","_debug_options_count":4},{"id":44564,"question":"Un étudiant doit choisir 2 options parmi 6 proposées. Combien de choix différents peut-il faire ?","option_a":"12","option_b":"15","option_c":"30","option_d":"36","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une combinaison : C(6,2) = 6! \/ (2! × 4!) = 15.","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\": \"15\", \"c\": \"30\", \"d\": \"36\"}}","_debug_options_count":4}]