Quiz — perm.pdf

Question 1 sur 10 20:00

[{"id":66296,"question":"Combien de permutations différentes 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":66297,"question":"Vrai ou Faux : La permutation de 3 éléments est toujours égale à 6.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La permutation de 3 éléments est 3! = 6, mais si les éléments ne sont pas distincts, le résultat peut varier.","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":66298,"question":"Quelle formule permet de calculer le nombre d'arrangements de 5 éléments pris 3 à 3 ?","option_a":"A₅³ = 5! \/ (5-3)!","option_b":"A₅³ = 5! \/ 3!","option_c":"A₅³ = 5! × 3!","option_d":"A₅³ = 3! \/ 5!","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule des arrangements est Aₙᵏ = n! \/ (n-k)!. Ici, A₅³ = 5! \/ (5-3)! = 5! \/ 2!.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A₅³ = 5! \/ (5-3)!\", \"b\": \"A₅³ = 5! \/ 3!\", \"c\": \"A₅³ = 5!","_debug_options_count":4},{"id":66299,"question":"Vrai ou Faux : La factorielle de 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par convention, 0! = 1, ce qui est utile dans de nombreuses formules combinatoires.","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":66300,"question":"Combien de nombres de 4 chiffres peut-on former avec les chiffres 1, 2, 3 et 4 sans répétition ?","option_a":"12","option_b":"24","option_c":"36","option_d":"48","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une permutation de 4 éléments, donc 4! = 24 nombres possibles.","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":66301,"question":"Vrai ou Faux : Le nombre de permutations de n éléments avec répétition est toujours inférieur à n!.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Avec répétition, le nombre de permutations peut être supérieur à n! si certains éléments se répètent.","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":66302,"question":"Quelle est la valeur de 5! ?","option_a":"15","option_b":"60","option_c":"120","option_d":"240","option_e":"","option_f":"","bonne_reponse":"c","explication":"5! = 5 × 4 × 3 × 2 × 1 = 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\": \"15\", \"b\": \"60\", \"c\": \"120\", \"d\": \"240\"}}","_debug_options_count":4},{"id":66303,"question":"Vrai ou Faux : Les arrangements sont utilisés uniquement pour des ensembles de petits nombres.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les arrangements s'appliquent à tout ensemble, quel que soit sa taille, tant que n ≥ k.","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":66304,"question":"Combien de façons peut-on arranger 3 livres sur une étagère ?","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une permutation de 3 éléments, donc 3! = 6 façons.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"6\", \"c\": \"9\", \"d\": \"12\"}}","_debug_options_count":4},{"id":66305,"question":"Vrai ou Faux : La formule de la permutation est toujours n! \/ (n-k)!.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette formule s'applique aux arrangements, pas aux permutations simples. Pour les permutations, c'est n!.","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}]