We distribute 15 pennies to 3 boys and 2 girls in such a way

We distribute 15 pennies to 3 boys and 2 girls in such a way that (to be really unfair) we require that each of the girls gets at least one penny (but we do not insist on the same thing for the boys). In how many ways can we do this?

Solution

First, we give one penny to each girl.

We have 13 pennies left to be distributed any way we want.

In this \"balls and urns\" proble,, there are n = 13 balls in r = 5 urns.

There are

(n + r - 1)! / [(r-1)!(n!)] ways to distribute n balls in r urns.

Thus, here, there are

(13+5-1)!/[(5-1)!(13!)] = 2380 WAYS. [ANSWER]