\begin{definition}[Definition:Hat-Check Distribution/Definition 2]
$X$ has the '''hat-check distribution with parameter $n$''' {{iff}}:
:$\ds \map \Pr {X = k} = \dfrac {!k} {n! } \dbinom n k$
where:
:$!k$ is the subfactorial of $k$
:$\dbinom n k$ is the binomial coefficient.
\end{definition}