  We show that for the product of two fixed point free conjugacy classes, the
average number of cycles is always very similar. Specifically, our main result
is that for a randomly chosen pair of fixed point free permutations of cycle
types $\alpha$ and $\beta$, the average number of cycles in their product is
between $H_n-3$ and $H_n+1$, where $H_n$ is the harmonic number.
