Expected number of empty boxes, placing m balls into n boxes

Question

$m$ balls are placed into $n$ boxes at random with uniform probability. What is the expected number of empty boxes?

The link below presents the solution for the case when $m = n$. Unfortunately, I do not understand the solution sufficiently to extend it to the non-equal case.

Find: The expected number of urns that are empty

Answer 1

By linearity of expectation, the answer is $n$ (the number of boxes) times the probability that a given box remains empty (that is $(1-1/n)^m$).

I'm assuming the positions are independent.