Probability of m choose k from n objects

Question

Data is stored in $n$ memory blocks. A user reads the blocks in random order (uniform distribution). Find the probability that each block was read no more than $k$ times, provided that there were a total of $m$ readings.

Answer 1

The problem seems to be equivalent to : place randomly $m$ balls into $n$ urns, find the probability that no urn has more than $k$ balls.

This does not have a simple (exact) solution.