Permutation

A permutation of a Set is an arrangement of all of the set’s elements
in a row, that is, a list without repetition that uses every element of the set.

Number of Permutations = n!

k-Permutation

A k-permutation of $X$ is a non-repetitive list made from $k$ elements of $X$.

The expression $P(n,k)$ denotes the number of k-permutations of an n-element set

If $0\le k\le n$, then $P(n,k)=n(n-1)(n-2)\cdot \cdot \cdot (n-k+1)=\frac{n!}{(n-k)!}$ .