We have a set of n elements. We would like to assign them to k sub-sets, so that each sub-set has m elements. The number of all possible assignments is then \frac{n!}{k!(m!)^k}.

Can someone help me intuit this formula?

EDIT: I intuit the k! in the denominator, but not the rest.

EDIT2: Crap, I've got it ... writing it down somehow helps.