An equipment manager is cleaning up after the big game. He needs to organize 8 identical bats into 4 identical racks. How many ways are there for him to distribute the bats if each rack gets at least one bat?
I think this is a case of "partitioning" of 8 identical bats onto 4 identical racks with at least 1 bat/rack. The result of this distribution is 5 ways as follows:
5 + 1 + 1 + 1 = 8
4 + 2 + 1 + 1 = 8
3 + 3 + 1 + 1 = 8
3 + 2 + 2 + 1 = 8
2 + 2 + 2 + 2 = 8
