Abstract problem - mappings and ops

Hi,

Could anyone help with the following question please?

Let S be a set with four elements, for example S={w,x,y,z}.

a) How many distinct operations can be defined on S?

b) How many commutative operations can be defined on S?

c) How many operations possessing an identity can be defined on S?

d) How many operations possessing an identity and such that every element has an inverse can be defined on S?

I'm thinking for part a) the answer is 4 to the power of 16 but should i be specifying the operation involved eg * or composition. The rest has me stumped. I usually just complete a Cayley table and work from there but if a) is 4 to the power of 16, I don't think I'll be doing that!

Thanks in advance for any help with this.