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# Combination

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

where is a factorial (Uspensky 1937, p. 18). For example, there are combinations of two elements out of the set , namely , , , , , and . These combinations are known as k-subsets.

The number of combinations can be computed in the Wolfram Language using Binomial[n, k], and the combinations themselves can be enumerated in the Wolfram Language using Subsets[Range[n],k].

Muir (1960, p. 7) uses the nonstandard notations and .

Ball Picking, Binomial Coefficient, Choose, Derangement, Factorial, k-Subset, Multichoose, Multinomial Coefficient, Multiset, Permutation, String, Subfactorial

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## References

Conway, J. H. and Guy, R. K. "Choice Numbers." In The Book of Numbers. New York: Springer-Verlag, pp. 67-68, 1996.Muir, T. A Treatise on the Theory of Determinants. New York: Dover, 1960.Ruskey, F. "Information on Combinations of a Set." http://www.theory.csc.uvic.ca/~cos/inf/comb/CombinationsInfo.html.Skiena, S. "Combinations." §1.5 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 40-46, 1990.Uspensky, J. V. Introduction to Mathematical Probability. New York: McGraw-Hill, p. 18, 1937.

Combination

## Cite this as:

Weisstein, Eric W. "Combination." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Combination.html