Three passengers—two men and one woman—are to be seated on a bus with five available seats, one of which is specifically reserved for females. The woman may choose to sit in the reserved seat or any other seat. How many distinct seating arrangements are possible for these three individuals?

Explanation

Consider two scenarios: Scenario 1: The woman occupies the seat reserved for females. The two men then have 4 remaining seats to choose from. The number of ways to seat the men is the number of permutations of 2 men in 4 seats: 4P2 = 4 × 3 = 12 ways. Scenario 2: The woman does not sit in the reserved seat. She can sit in any of the other 4 seats (4 ways). The two men then occupy the remaining 3 seats in order: first man in 3 ways, second man in 2 ways. Total ways here are 4 × 3 × 2 = 24. Adding both scenarios, total seating arrangements = 12 + 24 = 36.