Theoretical distribution of a random variable

Question

Martin has $n$ words, and he wants to make a computer program that chooses for him $k$ words (and shows them to him), where $k \le n$, for as many times as he clicks a button until all of the words are shown at least once. Every time the words are chosen, some of them can be repeated. So, he needs to find after how many attempts all the words will be shown at least once. If the $X_{n,k}$ is the random variable that shows the number of series until all the words are shown at least once, what's the theoretical distribution of it?