Using Pascal’s triangle, it is easy to calculate the number of subsets of a given set that have a certain size.
A permutation of a set is a selection of the elements of the set in some order. The number of permutations of n objects is n!, that is, the factorial function defined by
n! = n(n− 1)(n− 2) . . .3 · 2 · 1, for n ≥ 1, and 0! = 1. Example 2.1. How many ways may 10 books be arranged on a shelf?