Kamis, 05 Maret 2009

COMBINATION

Combination

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k,"

_nC_k=(n; k)=(n!)/(k!(n-k)!),

where n! is a factorial (Uspensky 1937, p. 18). For example, there are (4; 2)=6 combinations of two elements out of the set {1,2,3,4}, namely {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. These combinations are known as k-subsets.

The number of combinations (n; k) can be computed in Mathematica using Binomial[n, k], and the combinations themselves can be enumerated in Mathematica using Subsets[Range[n],{k}].

Muir (1960, p. 7) uses the nonstandard notations (n)_k=(n; k) and (n^_)_k=(n-k; k).

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