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$⨍:A→A, A= \{x_{1}, x_{2}, x_{3}, x_{4}\}$ then number of one - one functions so that $f (x) \neq x, \forall x \in A$ is

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Detailed Solution

$n (A) = 4$

Number of one - one functions so that $f (x) \neq x, \forall x \in A$ is

$4! (\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!}) = 12 - 4 + 1 = 9$

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