Quiz — Série d'exercices - Math dénombrement - 3ème Math (2012-2013) Mr Abderrazek Berrezig.pdf

Question 1 sur 10 20:00

[{"id":27910,"question":"Combien de permutations différentes peut-on former avec les lettres du mot 'MATH' ?","option_a":"12","option_b":"24","option_c":"6","option_d":"48","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 4 lettres distinctes, donc le nombre de permutations 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\": \"6\", \"d\": \"48\"}}","_debug_options_count":4},{"id":27911,"question":"Dans un groupe de 5 élèves, combien de façons peut-on choisir 2 délégués ?","option_a":"10","option_b":"20","option_c":"15","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une combinaison car l'ordre n'a pas d'importance. Le nombre de façons est C(5,2) = 5! \/ (2! × 3!) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"10\", \"b\": \"20\", \"c\": \"15\", \"d\": \"5\"}}","_debug_options_count":4},{"id":27912,"question":"Le nombre d'arrangements de 3 éléments parmi 4 est égal à 12.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le nombre d'arrangements est A(4,3) = 4! \/ (4-3)! = 24, donc l'affirmation est fausse.","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":27913,"question":"Quel est le coefficient binomial C(6,3) ?","option_a":"15","option_b":"20","option_c":"18","option_d":"12","option_e":"","option_f":"","bonne_reponse":"a","explication":"C(6,3) = 6! \/ (3! × 3!) = (6×5×4)\/(3×2×1) = 20.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"15\", \"b\": \"20\", \"c\": \"18\", \"d\": \"12\"}}","_debug_options_count":4},{"id":27914,"question":"Si on lance 3 dés à 6 faces, combien de résultats différents peut-on obtenir ?","option_a":"216","option_b":"18","option_c":"36","option_d":"108","option_e":"","option_f":"","bonne_reponse":"a","explication":"Chaque dé a 6 résultats possibles. En appliquant le principe multiplicatif, on obtient 6 × 6 × 6 = 216 résultats.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"216\", \"b\": \"18\", \"c\": \"36\", \"d\": \"108\"}}","_debug_options_count":4},{"id":27915,"question":"La formule de la factorielle de n est n! = n × (n-1) × ... × 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition exacte de la factorielle de 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":27916,"question":"Combien de nombres à 3 chiffres peut-on former avec les chiffres 1, 2, 3, 4 et 5 sans répétition ?","option_a":"20","option_b":"60","option_c":"120","option_d":"25","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un arrangement de 3 chiffres parmi 5. Le nombre de façons est A(5,3) = 5! \/ (5-3)! = 60.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"20\", \"b\": \"60\", \"c\": \"120\", \"d\": \"25\"}}","_debug_options_count":4},{"id":27917,"question":"Le principe multiplicatif s'applique uniquement aux combinaisons.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le principe multiplicatif s'applique à toutes les situations où une tâche est décomposée en étapes indépendantes, pas seulement aux 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":27918,"question":"Quel est le nombre de sous-ensembles d'un ensemble à 4 éléments ?","option_a":"8","option_b":"16","option_c":"4","option_d":"32","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un ensemble à n éléments a 2^n sous-ensembles. Pour n=4, 2^4 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8\", \"b\": \"16\", \"c\": \"4\", \"d\": \"32\"}}","_debug_options_count":4},{"id":27919,"question":"Si on a 5 chemises et 3 pantalons, combien de tenues différentes peut-on former ?","option_a":"8","option_b":"15","option_c":"20","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"En appliquant le principe multiplicatif, on obtient 5 × 3 = 15 tenues différentes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8\", \"b\": \"15\", \"c\": \"20\", \"d\": \"12\"}}","_debug_options_count":4}]