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:

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

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.