Solution to Determine the number of bijective functions f from {1, 2, . . . , 8} … - Sikademy
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Archangel Macsika

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

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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

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Question ID: mtid-5-stid-8-sqid-1309-qpid-1047