I'm trying to find out the name of a distribution that is like negative binomial, only for finite population and without replacement. Or like Hypergeometric distribution where the last event has to be a success.
Let's say we have $N$ balls in an urn, where $W$ of them are white balls and $B$ are black balls. I want to know what are the chances of needing to draw exactly $n$ balls so it is the first time I got $k$ of the $n$ drawn balls to be black (e.g: that the last ball drawn was black, and a total of $k$ out of $n$ are black).
I can't seem to find the name of such a distribution, so if you could also advise me on where to find names of distributions, that would also be lovely.