In a building, an elevator starts from the ground floor (that is, 0th floor) with 10 passengers and stops at every floor until the 15th floor which is the topmost floor. No new passengers enter the elevator on any floor from the 1st through the 15th floor. If all the passengers got off the elevator then the probability that at most one passenger got off at each floor is

Step-by-step solution

Total number of passengers is 10 . Total number of floors where passengers can get off is 15 (from the 1st to the 15th floor). Since each passenger can get off at any of the 15 floors, the total number of ways for the 10 passengers to get off is 15¹⁰ . The condition that at most one passenger gets off at each floor implies that all 10 passengers must get off at 10 distinct floors. The number of ways to choose 10 floors out of 15 is ¹⁵C₁₀ . The number of ways the 10 passengers can be arranged in these 10 chosen floo