Given the number of combinations w/o repetition for a set of size n from which you choose k is given by:
n! / k! * (n - k)!
How does one calculate the number of these combinations that include a given element. That amount should be the same for all elements of the original set.
For example, given the set {A, B, C, D}, there are 6 different ways to pick 2 elements: AB, AC, AD, BC, BD, CD. However there are only 3 of these subsets with 'A' in it (AB, AC, AD). I am stumped on getting to this 3 beyond brute forcing it.
I assume I am missing some formula?