(algorithm)

**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.*

Author: PEB

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Entry modified 2 March 2015.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul E. Black, "combination", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 2 March 2015. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/combination.html