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

Let the 4 boxes be B-1, B-2, B-3, B-4
Each box has 3 red balls and 2 blue balls

10 balls can be chosen in
Case-(1): when exacts one box gives four balls
Case-(2): when exacts two boxes gives three balls
Required no.of ways=No. of ways in case (1)+No. of ways in case (2)