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 \(2,3,...100\) enters the hall after the \((n-1)\)-th person has seated. He seats in seat number \(n\) if he finds it vacant; otherwise he takes an unoccupied seat at. Find the total number of ways in which the \(100\) seats can be filled up, provided the \(100\)-th person occupies seat number \(100\).