> [!NOTE] Definition 1 > Let $A$ be a [[Finite Set|finite set]] with [[Cardinality|cardinality]] $n\in\mathbb{N}^{+}.$ Let $k\in\mathbb{N}^{+}$ such that $k\leq n.$ An ordering of length $k$ of elements of $A$ (or $k$-permutation of $A$ - $n$ letters) is an [[Injection|injective]] [[List|list]] of length $k$ whose elements are taken $A.$ # Properties An $n$-permutation of $n$ letters is simply a [[Permutation of Finite Degree|permutation of n letters]]. By [[Number of k-Permutations of n Letters (Injections between Finite Sets)]], there are $\frac{n!}{(n-k)!}$ $k$-permutations of $n$ letters.