Statistics and Probability Dictionary

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Combination

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can select 2 letters from that set. Each possible selection would be an example of a combination. The complete list of possible selections would be: AB, AC, and BC.

Computing the number of combinations. The number of Combinations of n objects taken r at a time is
nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)! = nPr / r!

Note that AB and BA are considered to be one combination, because the order in which objects are selected does not matter. This is the key distinction between a combination and a permutation. A combination focuses on the selection of objects without regard to the order in which they are selected. A permutation, in contrast, focuses on the arrangement of objects with regard to the order in which they are arranged.

See also:   Rules of Counting | Event Counter