1. How many permutations of \(\{1, 2, 3, 4, 5\}\) have \(2\) in the second place?

Fix the \(2\) in the second place and permute the remaining 4 elements for the total of \(4! = 24\) permutations.

2. How many permutations of \(\{1, 2, ..., n\}\), \(n > 3\), have \(2\) in the second place and \(3\) in the third place?

Fix \(2\) in the second place and \(3\) in the third place and permute the remaining \(n - 2\) elements for the total of \((n - 2)!\) permutations.