Let $n, m \in \mathbb{N}$ each be a D996: Natural number such that

(i)	\begin{equation} m \leq n \end{equation}
(ii)	$\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})$ is the D2222: Set of injections from $\{ 1, \ldots, m \}$ to $\{ 1, \ldots, n \}$

Then \begin{equation} |\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})| = m ! |\mathcal{P}_m \{ 1, \ldots, n \}| \end{equation}

Let $n, m \in \mathbb{N}$ each be a D996: Natural number such that

(i)	\begin{equation} m \leq n \end{equation}
(ii)	$\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})$ is the D2222: Set of injections from $\{ 1, \ldots, m \}$ to $\{ 1, \ldots, n \}$

Then \begin{equation} |\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})| = m ! \binom{n}{m} \end{equation}