How do you solve a permutation in math?

If there are n objects to fit r places (e.g. 9 people in 7 chairs, 4 tumblers in a lock) then the number of permutations is nCk, stated as n-choose-k.

This number can be calculated by the formula n!/(n - k)!. If k is equal to n, then (n - k)! = 0! = 1, and the number of permutations is simply n!. If the direction of the permutation is irrelevant (e.g. ABCD is the same as DCBA) then divide by two to cancel out the double-counting.