There are n! permutations of a set of n elements. For example, the set {A, B, C} has 3! = 6 permutations: ABC, ACB, BAC, BCA, CAB, and CBA. There are (n + 1)! permutations of the set after we add a...

There are n! permutations of a set of n elements. For example, the set {A, B, C} has 3! = 6 permutations: ABC, ACB, BAC, BCA, CAB, and CBA. There are (n + 1)! permutations of the set after we add a new target. Argue that, if each of these permutations is equally likely, each of the n + 1 places where the target might belong is equally likely.