Consider a jar with $N$ indexed balls from $1$ to $N$ and the variable $X=\max\{x_1,\dots,x_n\} $ where $n<N$ is the number of balls we took out without replacement.
I found that $P(X=k)=\begin{cases} 0 &\text{ if } k<n\\ \frac{{k-1\choose n-1}}{N\choose n-1} &\text { if } n\le k\le N \end{cases}$
Is $X$ related to the negative binomial distribution, and how?