Definition:Combination
From ProofWiki
Definition
Let $S$ be a set containing $n$ elements.
An $r$-combination of $S$ is a subset of $S$ which has $r$ elements.
From Cardinality of Set of Subsets, we have that the number of $r$-combinations of $S$ is $\displaystyle \frac {n!} {r! \left({n - r}\right)!} = \binom n r$.
Sources
- George E. Andrews: Number Theory (1971): $\S 3.1$: Definition $3.2$
