# Combination

**Combinations**are studied in combinatorics: let

*S*be a set; the combinations of this set are its subsets. A

*k*-combination is a subset of

*S*with

*k*elements. The order of listing the elements is not important in combinations: two lists with the same elements in different orders are considered to be the same combination. The number of

*k*-combinations or

*k*-subsets of set with

*n*elements is the binomial coefficient "

*n*choose

*k*", written as

_{n}C

_{k},

^{n}C

_{k}or as

*n*,

*k*).

One method of deriving a formula for _{n}C_{k} proceeds as follows:

- Count the number of ways in which one can make an ordered list of
*k*different elements from the set of*n*. This is equivalent to calculating the number of*k*-permutations. - Recognizing that we have listed every subset many times, we correct the calculation by dividing by the number of different lists containing the same
*k*elements:

*n*,

*k*) can also be found using Pascal's triangle, as explained in the binomial coefficient article.