|This is an AoPSWiki Word of the Week for Nov 1-7|
A combination is a way of choosing objects from a set of where the order in which the objects are chosen is irrelevant. We are generally concerned with finding the number of combinations of size from an original set of size
The common forms of denoting the number of combinations of objects from a set of objects is:
Consider the set of letters A, B, and C. There are different permutations of those letters. Since order doesn't matter with combinations, there is only one combination of those three. In general, since for every permutation of objects from elements , there are more ways to permute them than to choose them. We have , or .