Let S = {a, b, c, d}.

How many binary operations can be defined on S?

I think the answer might be $\displaystyle 4^{16}$

How many are commutative?

I think the answer is $\displaystyle 4^{10}$

Assume that x = x * a = a * x for all x in the set S.

Then how many binary operations are there?

I think the answer is $\displaystyle 4^{9}$

Can any1 tell me if my answers are right or wrong?