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 \(P \bmod Q \).

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