One hundred passengers line up to board an airplane with 100 seats. Each passenger is to board the plane individually, and must take his or her assigned seat before the next passenger may board. However, the passenger first in line has lost his boarding pass and takes a random seat instead. This passenger randomly selects another unoccupied seat each time it appears that he is not occupying his assigned seat. Use simulation to find the probability of the passenger changing seats five or more times before getting to his assigned seat. Hint: number the passengers in line as 1, 2,..., 100 and number their assigned seats accordingly.