Below is the problem that I wanted to solve

When there are $m$ balls and $n$ bins, balls are thrown into bins where each ball is thrown into a bin uniformly at random. What is the expected number of bins that contain strictly more than 1 ball?

What I am understanding so far is that, each ball toss will be independent, and expected number of balls in each basket will be $m/n$. But this does not seem to help me solving the problem.

I heard this is very similar to the birthday problem, but with different number of bins and arbitrary number of balls.

How should I approach solving this problem?