Assume that there are $m$ balls and $n$ urns with $m\gt n$. Each ball is thrown randomly and uniformly into urns. That is, each ball goes into each urn with probability $\dfrac1n$.
What is the probability that there are exactly $r$ urns with at least one ball in it? In other words, what is the probability that there are $n-r$ empty urns?
( I am Not sure whether it makes any difference whether balls and urns being distinguishable or not. If there is a difference assume that both balls and urns are distinguishable)