[Solved] Let I_6=1,2,3,4,5,6 . How many permutations of I_6 have the even numbers in the correct positions (i.e. 2 is in the 2^text nd position, etc.)?


Question: Let \(I_{6}=1,2,3,4,5,6 .\) How many permutations of \(I_{6}\) have the even numbers in the correct positions (i.e. 2 is in the \(2^{\text {nd }}\) position, etc.)? How many permutations of \(I_{6}\) have the even numbers in even-numbered positions?

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