The number of ways of picking unordered outcomes from possibilities. Also known as the binomial
coefficient or choice number and read " choose ,"
is a factorial (Uspensky 1937, p. 18). For example,
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 .
See alsoBall Picking
, Binomial Coefficient
Explore with Wolfram|Alpha
ReferencesConway, J. H. and Guy, R. K. "Choice Numbers." In The
Book of Numbers. New York: Springer-Verlag, pp. 67-68, 1996.Muir,
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.
Cite this as:
Weisstein, Eric W. "Combination." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Combination.html