Combination (original) (raw)
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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 
.
See also
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." ยง1.5 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.
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Cite this as:
Weisstein, Eric W. "Combination." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Combination.html