Cardinality of Set of Injections

Theorem
Let $S$ and $T$ be sets.

The number of injections from $S$ to $T$, where $\left|{S}\right| = m, \left|{T}\right| = n$ is often denoted $P_{nm}$, and is:


 * $ {}^m P_n = \begin{cases}

\dfrac {n!} {\left({n - m}\right)!} & : m \le n \\ 0 & : m > n \end{cases}$