A={1,2,3,4,5,6};How many bijective functions $f:A->A$ have the property that $f(1)!=2$ ?

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Answer 1 · 2017-03-26T10:57:00

$600$

A bijective function from a finite set to itself is a permutation.

There are a total of $6!$ permutations of $6$ objects, of which exactly $1/6$ map $1$ to $2$ .

So the answer is:

$6!*(5/6) = 5!*5 = 120*5 = 600$

A={1,2,3,4,5,6};How many bijective functions f:A->Af:A->Ahave the property that f(1)!=2f(1)!=2?