This is problem 4 from section 2.3 of Fundamentals of Probability by Saeed Ghahramani. 1. The problem statement, all variables and given/known data Robert has eight guests, two of whom are Jim and John. If the guests will arrive in a random order, what is the probability that John will not arrive right after Jim? 2. Relevant equations ... 3. The attempt at a solution There are 8! ways for the guests to arrive. There are 7 ways for John to arrive right after Jim. The probability of John arriving right after Jim is then 7/8!, and the probability of John not arriving right after Jim is 1-7/8!=0.9998. I am pretty sure it is right, but not 99.98% sure.