In how many ways can 5 people be seated in 5 adjacent seats in a theater?
Answer
Have the youngest sit first, then the next youngest, and so on. The first person has 5 choices. No matter where the first person sits, the next person has 4 choices. No matter where the first two people sit, the third person has 3 choices. The fourth person then has 2 choices. The fifth person then has 1 choice. Therefore, there are \(5\cdot 4\cdot 3\cdot 2\cdot 1 = \boxed{120}\) ways for the five people to sit.
Step 1 ：Have the youngest sit first, then the next youngest, and so on. The first person has 5 choices. No matter where the first person sits, the next person has 4 choices. No matter where the first two people sit, the third person has 3 choices. The fourth person then has 2 choices. The fifth person then has 1 choice. Therefore, there are \(5\cdot 4\cdot 3\cdot 2\cdot 1 = \boxed{120}\) ways for the five people to sit.
