I know how to find number of permutations with cycle. And I'm not sure, but for 2 it should be something like this
$\sum_{k=1}^{n=1} \binom{n}{k} (k-1)!(n-k-1)! $
But I have a problem with 3 cycles. And is there exist any general formula for number of permutations for n elements with k cycles?