1. The problem statement, all variables and given/known data If Sam and Peter are among n men who are arranged at random in a line, what is the probability that exactly k men stand between them?" 2. Relevant equations Not sure. 3. The attempt at a solution This is driving me insane. I listed out the possibilities for n = 3, and it looked to me like Peter and Sam could surround n men 2(n-k-1) ways. Since there are n! possible lines, I said: p = 2(n-k-1)/n! But the book says p = 2(n-k-1)/n(n-1) The frustrating thing is that our answers are equal for n=3, but obviously not for higher values of n. I started trying to do it concretely for n=4, but there were so many possibilities that I got too confused. It's just killing me, because I know the formula I came up with for n=3 was just a guess based on my empirical observation of the outcomes. I don't know how to do this problem "theoretically." What am I doing wrong? Thanks.