Question

In how many ways can 12 identical action figures be given to five children if each child recieves at most 3 action figures?

Answer 1

Let's solve the inverse problem: in how many ways can three figures be taken from five children if each has three ones? Finally they'll have twelve figures, and no more than three figures each. We can take off each of three figures from each of five children. So, we can do that in N = 5*5*5 = 5^3 ways.