# Expected number of unique selections

If I'm selecting $N$ elements uniformly at random (with replacement) from $\{1, \dots, M\}$, what is the expected number of values that are selected exactly once?

The basis for this question originated here.

Hint: Expected value is linear. What is the probability that a particular value is selected exactly once?

• Is that $$\Big({M-1\over M}\Big)^{N-1} \;\;\;\; ?$$ – Aqua Nov 2 '17 at 19:30