In mathematics, a k-element combination drawn from a set with elements, is a subset of having elements that is unordered and without repetitions.
Combinations are closely related to k-permutations, the difference being that for k-permutations order matters.
k-combinations of n are denoted
The number of possible k-combinations of n is:
This is derived from what we know about k-permutations of n, specifically that the number of k-permutations of n is:
For each -sized subset of there are permutations. Since order does not matter with combinations, these permutations are actually all the same combination. This explains the term in the denominator of the – it accounts for the fact that there are permutations for every -sized subset we can choose from set .
The values represented by are also known as the binomial coefficients, denoted and read, “n choose k.”« Back to Glossary Index