Permutation

Abstract

The arrangement of objects where order matters
Given $n$ objects, there is a total $n!$ permutations. For example, given 3 objects ${a, b, c}$ , the total number of permutations is $6$ - ${a, b, c}$ , ${b, a, c}$ , ${c, a, b}$ , ${a, c, b}$ , ${b, c, a}$ , ${c, b, a}$

A pair of elements that are out of order relative to each other compared to their natural order in sorted permutation
For example, given a permutation ${3, 1, 2}$ , the pairs $(3, 1)$ and $(3, 2)$ are inversions because $3$ comes before both $1, 2$

Indicate Chaoticness

The number of inversions in a permutation can indicate how far the permutation is from being sorted