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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?