Barclays Analyst interview questions

n numbered places in a bus, n people with a ticket for one place each come in at random. k of them are anarchists who sit down in a random free seat. All other people sit down in the seat assigned on the ticket, unless it's already taken, in which case they sit down at random. What is the probability that x people are in their assigned seat? (I think original question was with n=10, k=1, and x=10).