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Given a set A, an element x∈A, and a function f:A→A, x is a fixed point...

Given a set A, an element x∈A, and a function f:A→A, x is a fixed point for f if f(x) = x.
Suppose A = {♥,♦, ♣,♠}. How many functions are there mapping A to A for which ♥ is a fixed point?
How many for which ♥ and♦ are fixed points?
♥,♦ and ♣?
How about functions for which all four elements are fixed points?

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