Permutations are arrangements of items where the order of the items matters.

The number of ways of permuting r items from a set of n items is similar to the n! for ordering n items, but we have to stop the multiplication after r items - when there are (n−r) remaining items.

The number of permutations is thus:

Example

Anna is setting a new 4 digit pin code on her mobile phone. How many possible codes can she make if she does not reuse any digits?

There are n=10 digits (0−9), and the pin length is r=4. The order of the digits does matter, and digits cannot be reused, so the number of possible codes is

(using a calculator)