Definition: Choose m of n elements, where m ≤ n.

See also permutation, subset.

Note: A combination is a subset with exactly m elements.

There are n!/(n-m)!m! combinations of n (distinguishable) elements taken m at a time. Why? To begin, there are n! permutations. Permutations that only differ in the order of the n-m elements not taken are the same combination, so divide by (n-m)!. The order of the m elements taken doesn't matter either, so divide by m!, too.

Author: PEB

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Entry modified 2 March 2015.
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Cite this as:
Paul E. Black, "combination", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 March 2015. (accessed TODAY) Available from: