Randomly select an element from a list

Question

Suppose I have a list that contains N elements, every time I randomly select an element from it and mark it as visited. What is the expected number of selection that I have to make until all the elements in the list are marked as visited?

Answer 1

With $N$ elements, the expected number of selections you have to make is

$$N \displaystyle\sum_{k=1}^N \frac{1}{k}$$

As was noted in the comments, this is called the coupon collector's problem.