In combinatorial mathematics, a combination is an un-ordered collection of unique elements. Given S, the set of all possible unique elements, a combination is a subset of the elements of S. The order of the elements in a combination is not important (two lists with the same elements in different orders are considered to be the same combination). Also, the elements cannot be repeated in a combination (every element appears uniquely once). A k-combination (or k-subset) is a subset with k elements. The number of k-combinations (each of size k) from a set S with n elements (size n) is the binomial coefficient.

A combination is a special case of a partition of a set; specifically, a partition into two sets of size k and n-k.

See also

• Combinadic
• Combinations and permutations
• Multiset

Combinatorics

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