suppose you randomly permute the numbers 1, 2, . . . , 100. that is, you select a permutation uniformly at random. what is the probability that the number 75 ends up in the 45-th position in the resulting permutation? (for example, in the permutation 1, 3, 2, 5, 4 of the numbers 1 . . . 5, the number 2 is in the 3rd position in the permutation and the number 4 is in the 5th position.)