Combination

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For other uses, see Combination (disambiguation).

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

<math> C_k^n = {n \choose k} = \frac{n!}{k!(n-k)!}</math>.

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

[edit] See also

• Permutation
• Combinadic
• Permutations and combinations
• Multiset

[edit] External links

• Many Common types of permutation and combination math problems, with detailed solutions

fr:Combinaison ko:조합 it:Combinazione lv:Kombinācija nl:Combinatie (wiskunde) ja:組合せ (数学) pl:Kombinacja bez powtórzeń pt:Combinação sem repetição ru:Сочетание sr:Комбинација fi:Kombinaatio sv:Kombination (matematik) zh:組合