For a Hypergeometric random variable with \(R\) = {0, 1, ..., r} and assuming \(n_1 \ge r\) and \(n-n_1 \ge r\text{,}\)

\begin{equation*} f(x) = \frac{\binom{n_1}{x} \binom{n-n_1}{r-x}}{\binom{n}{r}} \end{equation*}