# Permutation

The factorial has special application in defining the number of permutations in a set which does not include repetitions. The number n! is precisely the number of ways we can rearrange n things into a new order. For example, if we have three fruit: an orange, apple and pear, we can eat them in the order mentioned, or we can change them e.g. an apple, then a pear and finally an orange. The exact number of permutations is then ${\displaystyle 3!=1\cdot 2\cdot 3=6}$. The number gets extremely large as the number of items (n) goes up.