1. How many cyclic permutations are there of set with n elements

2. Permutation has k cycles of powers

show that: a)

for 1.. isn't it just simply n! if the cyclic permutation is defined as one with just 1 cycle and if it's defined as one with just one and only cycle that has more than 2 elements in it? how to prove it if it's true?

2. No idea, also power of cycle tells us how many elements each cycle has, right?