jee-advanced 2022 Q15

jee-advanced · India · paper2 3 marks Combinations & Selection Selection with Group/Category Constraints
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?
(A) 21816
(B) 85536
(C) 12096
(D) 156816
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?

(A) 21816\\
(B) 85536\\
(C) 12096\\
(D) 156816