Cardinality of Set of Injections

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

The number of injections from $S$ to $T$, where $\card S = m, \card T = n$ is often denoted ${}^m P_n$, and is:


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

\dfrac {n!} {\paren {n - m}!} & : m \le n \\ 0 & : m > n \end{cases}$