Answer to Question #254771 in Discrete Mathematics for Vishnu Kumar

Question

Determine the number of bijective functions f from {1, 2, . . . , 8} to itself such that f(i) 6= i for any even number i.

Answer 1

the number of bijective functions f from {1, 2, . . . , 8} to itself such that f(i) $\neq$ i for any even number i.

The total number of bijective functions:

$N=8!=40320$  

There are 4 even numbers in the set, so the number of bijective functions such that f(i)=i:

 $n=(8-4)!=24$

Answer:

$N-n=40320-24=40296$