The hypergeometric distribution:

  Suppose a population of size N has M units labelled as ``success'' and N-M labelled as ``failure.'' A sample of size n is drawn without replacement. The random variable X is defined as the number of ``successes'' in the sample.

The probability mass function for X is

$$p_X (x) \; = \; \frac{ \left( \begin{array} {c} M \\ x \end... ...rray} \right) } , \quad x = 0 , 1 , \ldots , \min \{ n , M \} ,$$

and otherwise.