There's a long table and behind it - a long bench. The only way to sit and get up and leave from the bench is through one side. Behind the table, there are 14 students and they're writing an exam. Any of them, who finishes their work, gets up, asks for their friends to let them through one by one and leaves. What is the possibility that 9th student (counting from the exit side) won't have to 'apologise' to their friends while leaving?
The way I see it, the possibility is $1/256$, since there are $8$ people blocking the exit, so the student will have to either apologise or not apologise ($2$ outcomes) to $8$ people, that makes $256$ total outcomes. I know for a fact that this solution is incorrect, but don't really know how to solve this correctly. Any tips?