Hypergeometric Distribution

Hypergeometric distribution counts the number of ways you can obtain particular target values when sampling from a population without replacement.

This describes many systems - most notably a deck of 52 Cards (e.g. poker hands).

Hypergeometric distribution:

$\displaystyle {\dfrac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}}$

where:

${\begin{aligned}K&=&{\mbox{Successes}}\\N&=&{\mbox{Pop. size}}\\k&=&{\mbox{Targets}}\\n&=&{\mbox{Sample size}}\end{aligned}}$