Cardinality of Set of Subsets

Theorem
Let $S$ be a set such that $\left|{S}\right| = n$.

Let $m \le n$.

Then the number of subsets $T$ of $S$ such that $\left|{T}\right| = m$ is:
 * ${}^m C_n = \dfrac {n!} {m! \left({n - m}\right)!}$

Also see

 * Definition:Binomial Coefficient


 * Binomial Theorem