A partial permutation is an ordering of only $k$ objects selected from a collection of $n$ objects ($k \leq n$).
For example, a partial permutation of 3 of the first 8 positive integers is given by $(5, 7, 2)$.
The statistic $P(n, k)$ counts the total number of possible partial permutations of $k$ objects chosen
from a collection of $n$ objects.
