> [!NOTE] Definition (Combination of $k$ elements of a finite set) > Let $A$ be a [[Finite Set|finite set]] of [[Cardinality|cardinality]] $n\in \mathbb{N}^{+}.$ Let $k\in \mathbb{N}^{+}$ such that $k\leq n.$ Then a combination of $k$ elements of $A$ is a [[Subsets|subset]] of $k$ elements. # Properties By [[Number of k-Combinations of n Letters]], $|C_{n,k}(A)| = \frac{n!}{k!(n-k)!}$ where $C_{n,k}(A)$ denotes the set of all combinations of $k$ elements of $A.$