There are 100 people in a queue waiting to enter a hall. The hall has exactly 100 seats numbered from 1 to 100. The first person in the queue enters the hall, chooses any seat and sits there. The n-th person in the queue, where n can be 2,...,100, enters the hall after (nā1)-th person is seated. He sits in seat number n if he finds it vacant; otherwise he takes any unoccupied seat. Find the total number of ways in which 100 seats can be filled up, provided the 100-th person occupies seat number 100. combinatorics unsolvedcombinatorics