Section 6.4: Counting Subsets of a Set: Combinations

In section 6.2, we learnt how to count the number of r-permutations from an n-element set (recall that an r-permutation is an ordered selection of r elements from a set containing n elements). Note that a permutation depends upon ordering that is, if x, y ∈ S, a set, then the permutation x, y is different to that of y, x. In this section, we introduce a similar notion to a permutation called a combination, where order does not matter i.e. so x, y and y, x would be considered the same. The idea of a combination is helpful when calculating probabilities of events where the order of choices does not matters (so hands in poker for example).