A permutation is a change or variation, like the many possible permutations of hair color you get when you start experimenting with different dyes.
Permutation is made of the prefix per for "thoroughly" and mutation, which means “change.” A permutation is a thorough change of something, like a substitution. Asking a waiter to give you sweet potato fries instead of regular fries is a permutation. Switching hats with a friend is a permutation. If you switch hats with five of your friends, you'll have many fashion permutations to choose from. Permutations are also like replacements or switches.