# Inversion 2

In a permutation $$a_{1}, a_2, \ldots, a_{n}$$ of $$n$$ distinct integers, an inversion is a pair $$(a_{i}, a_{j})$$ such that $$i < j$$ and $$a_{i} > a_{j}$$.

If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of $$1,2,3,\ldots,n$$?

×