What are the number of ways in which 3 different boxes can be filled with 5 different balls so that one box gets 3 balls and the other two get 1 ball each? Each box has the capacity to hold 5 balls at most. The answer to this is 5!/(3!1!1!) x 1/2! x 3! = 60 But when I do it, I think of it this way- (Number of ways to chose 3 balls out of 5) x (Number of ways to chose 1 ball out of 2) x (Number of permutations of boxes) = C(5,3) x C(2,1) x 3! = 5! = 120. But this is wrong as one can easily see. So how do I go about the right way?