Hypergeometric Distribution

Notation:

$X \sim Hypergeometric(N, K, n)$

Probability Mass Function:

$P(X=x)=\dfrac{{K \choose x} {N - K \choose n - x}}{ {N \choose n} }$

where:

$N$ is the population size,
$K$ is the number of success states in the population,
$n$ is the number of draws (i.e. quantity drawn in each trial),
$x$ is the number of observed successes.
$N \in \{ 0, 1, 2, \ldots \}$
$K \in \{ 0, 1, 2, \ldots, N\}$
$n \in \{ 0, 1, 2, \ldots, N\}$
$x \in \{ max(0, n + K -N), \ldots, min(n, K) \}$

Mean:

$\mathrm{E}[X]=n\dfrac{K}{N}$

Variance:

$\mathrm{Var}[X]=n\dfrac{K}{N}\dfrac{(N-K)}{N}\dfrac{N - n}{N - 1}$

References: