Combination without Repetition

combinatorics

Definition

Combination without Repetition

A combination without repetition is an unordered selection of $k$ elements out of $n$ elements or a subset of size $k$ from a set of size $n$.

All possible combinations of a set of length $n$ can be counted using the binomial coefficient:

$$\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\frac{n!}{k!(n-k)!}$$

by the product rule.