combination

In probability and statistics, a combination refers to the total number of ways a subset of a particular size can be chosen from a larger set, where the order of choice does not matter. The general formula is given by

    C(n,r) = n! / ((n−r!) × r!)
        where n! is n factorial, that is n × (n−1) × (n−2) × ... × 3 × 2 × 1

The term C(n,r) is sometimes spoken as "n choose r", and written Cⁿ_r.

For example, given four letters A, B, C, D, there are precisely six combinations of two items: AB, AC, AD, BC, BD, CD.
    C(4,2) = 4! / ((4-2) × 2!) = 4×3×2×1 / ( 2×1 × 2×1 ) = 24 / (2 × 2 ) = 6

Combinations are related to permutations, but the latter counts the number of ordered selections.