Working my way through a combinatorics text and I'm hung up on a couple of questions:
1.) Let $p=p_1 p_2\cdots p_n$ be a permutation. An inversion of $p$ is a pair of entries $(p_i,p_j)$ so that $i
2.) Let $I(n,k)$ be the number of $n$-permutations that have $k$ inversions. Prove that $I(n,k)=I(n,\binom{n}{2}-k)$.
3.) Find an explicit formula for $I(n,3)$.
These are from a combinatorics text, but I vaguely remember this topic popping up in undergrad abstract algebra and possibly in an algorithm design course as well.