Bad Shuffle

Consider the following algorithm, which generates a (not necessarily uniformly) random permutation of numbers $1$ through $N$: ``` P := [1, 2, ..., N] for i in 1..N do j := rand(1, N) swap(P[i], P[j]) ``` Here, `rand(1, N)` returns a uniformly random integer between $1$ and $N$ inclusive. Let's denote the probability that the permutation generated by this algorithm is $P$ by $p(P)$. Fin