# Combination of Functions

Let a function $$f$$ be defined as $$f: \{1,2,3,4\} \to \{1,2,3,4\}$$.

If $$f$$ satisfies $$f(f(x)) = f(x)$$ for all $$x\in \{1,2,3,4\}$$, then the number of such functions $$M$$ and the probability of selecting a bijective function is $$N$$.

Given that $$M +N$$ can be expressed as $$\dfrac PQ$$, where $$P$$ and $$Q$$ are coprime positive integers, find $$P \bmod Q$$.

×