I encountered this problem in my probability class, and we weren't able to solve it, so I would like to know the answer.
If you have $m$ balls and $n$ boxes, with $n < m$, and you insert the balls into the boxes randomly, what is the probability that all the boxes have at least one ball in it?
The problem doesn't specify if the balls are distinguishable or not, so you may assume either, so another question would be, if you assume they are distinguishable will you get the same answer as assuming they are not distinguishable? (This would be great because I think the non-distinguishable case is easier).
I appreciate any insight on the problem.