Suppose I a set with $n$ items, $k$ of which have a certain property($k\leq n$), and I choose $m$ items randomly from that set($m\leq n$), what is the distribution of the number of chosen items having that property? An item can only be chosen once.
I expect an answer in the form $\left( \begin{array}{c} f(k,n,m) \\ g(k,n,m) \end{array} \right)$, but I don't know $f(k,n,m)$ and $g(k,n,m)$.