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.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 26 November 2007.
HTML page formatted Tue Dec 6 16:16:32 2011.
Cite this as:
Paul E. Black, "combination", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 26 November 2007. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/combination.html