Please forgive me if this looks like a trivial question; I'm quite sure this is a well known problem, but I don't know its formal name, so I've been so far unable to look it up on Google.
Given a set containing $X \cdot Y$ elements, how many ways there are of choosing $X$ disjoint (non-overlapping) subsets containing $Y$ elements each? Ordering of subsets is not relevant, thus each permutation of the same subsets should only appear once.