Cardinality of Set of Subsets

Theorem
Let $S$ be a set such that $\card S = n$.

Let $m \le n$.

Then the number of subsets $T$ of $S$ such that $\card T = m$ is:
 * ${}^m C_n = \dfrac {n!} {m! \paren {n - m}!}$

Also see

 * Definition:Binomial Coefficient


 * Binomial Theorem