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

Can someone help me intuit this formula?

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

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