pr.probability - Probability Question

You have $N$ boxes and $M$ balls. The $M$ balls are randomly distributed into the $N$ boxes. What is the expected number of empty boxes?

I came up with this formula:

$sum_{i=0}^{N}ibinom{N}{i}left(frac{N-i}{N}right)^{M}$

This seems to yield the right answer. However, it requires calculating large numbers, such as $binom{N}{frac{N}{2}}$. Is there a more direct way, perhaps using a probability distribution? It seems that neither the binomial nor the hypergeometric distributions fit the problem.

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