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

Question

4469 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-26T10:57:00

$600$ $600$

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

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

So the answer is:

$6! \cdot (\frac{5}{6}) = 5! \cdot 5 = 120 \cdot 5 = 600$ $6!*(5/6) = 5!*5 = 120*5 = 600$

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