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combination

A selection of items where order doesn't matter — counted by C(n,r).

A combination is a selection of items in which order does not matter, so rearranging the chosen items produces the same outcome. The number of combinations of r items chosen from n distinct items is C(n,r)=\binom{n}{r}=\dfrac{n!}{r!(n-r)!} — the permutation count P(n,r) divided by r! to remove the redundant internal orderings.

Examples

  • Choosing a 3-person committee from 5 people is a combination: C(5,3)=10.

See also

permutation
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