KöMaL 2023 B5338

There are 10 numbered seats in a particular row of an auditorium. The seats are accessible from each end of the row. The 10 spectators holding tickets for that row arrive in a random order and they take their seats. Since the spectators do not like passing others already seated, they will approach their seats from the direction where that can be avoided, if possible. Determine the probability that at least one of the 10 ticket holders will not be able to access their seat without passing a seated spectator.