How many different moore machines m s i o g s0 can be

Question

Question: Suppose that S, I , and O are finite sets such that |S| = n, |I | = k, and |O| = m.

a) How many different finite-state machines (Mealy machines) M = (S, I, O, ƒ, g, s₀) can be constructed, where the starting state s0 can be arbitrarily chosen?

b) How many different Moore machines M = (S, I, O, ƒ, g, s₀) can be constructed, where the starting state s0 can be arbitrarily chosen?