Dénombrements : testez vos connaissances en combinatoire

Question 1 sur 10 10:00

[{"id":78962,"question":"Combien de permutations existe-t-il pour 5 éléments distincts ?","option_a":"5","option_b":"24","option_c":"120","option_d":"625","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le nombre de permutations de n éléments est donné par n!. Ici, 5! = 5 × 4 × 3 × 2 × 1 = 120.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78963,"question":"Dans un arrangement de 4 éléments parmi 7, l'ordre est-il important ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, dans un arrangement, l'ordre des éléments est crucial, contrairement aux combinaisons où l'ordre n'a pas d'importance.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78964,"question":"Quelle est la valeur de C(6,2) ?","option_a":"15","option_b":"30","option_c":"6","option_d":"24","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(6,2) = 6! \/ [2!(6-2)!] = (6×5)\/(2×1) = 15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78965,"question":"Si une urne contient 3 boules rouges et 2 boules bleues, combien y a-t-il de façons de tirer 2 boules rouges ?","option_a":"1","option_b":"3","option_c":"6","option_d":"9","option_e":"","option_f":"","bonne_reponse":"B","explication":"C(3,2) = 3! \/ [2!(3-2)!] = 3 façons de choisir 2 boules rouges parmi 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78966,"question":"Le principe multiplicatif s'applique uniquement aux arrangements.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux, le principe multiplicatif s'applique à tous les types de dénombrement, pas seulement aux arrangements.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78967,"question":"Quelle formule donne le nombre d'arrangements de k éléments parmi n ?","option_a":"n! \/ k!","option_b":"n! \/ (n-k)!","option_c":"k! \/ n!","option_d":"(n+k)! \/ k!","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le nombre d'arrangements de k éléments parmi n est A(n,k) = n! \/ (n-k)!.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78968,"question":"Combien de codes à 4 chiffres peut-on former avec les chiffres 1 à 6 si les répétitions sont autorisées ?","option_a":"24","option_b":"1296","option_c":"360","option_d":"120","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour chaque chiffre, il y a 6 choix possibles. Avec 4 chiffres, cela donne 6^4 = 1296 codes possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78969,"question":"Dans une combinaison, l'ordre des éléments est-il pris en compte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux, dans une combinaison, l'ordre n'a pas d'importance. Seuls les éléments sélectionnés comptent.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78970,"question":"Quelle est la valeur de A(5,3) ?","option_a":"10","option_b":"60","option_c":"120","option_d":"20","option_e":"","option_f":"","bonne_reponse":"B","explication":"A(5,3) = 5! \/ (5-3)! = (5×4×3×2×1) \/ (2×1) = 60.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78971,"question":"Si on tire 3 cartes dans un jeu de 52 cartes, combien y a-t-il de combinaisons possibles ?","option_a":"1326","option_b":"22100","option_c":"52","option_d":"156","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(52,3) = 52! \/ [3!(52-3)!] = 22100 combinaisons possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]