How many ways can five people, A, B, C, D, and E, sit in a row at a concert hall if D and E will not sit next toeach other?
A) 72
B) 24
C) 48
D) 60

Question

Quizplus · Accepted Answer

First, calculate the total number of ways all five people can sit in a row without restrictions, which is 5! (5 factorial) = 120 ways. Then, calculate the number of ways D and E can sit next to each other. Treat D and E as a single unit, so there are 4 units to arrange (DE, A, B, C), which can be done in 4! = 24 ways. Within this unit, D and E can be arranged in 2! = 2 ways. So, the number of arrangements where D and E are next to each other is 24 * 2 = 48. Subtract this from the total arrangements to get the arrangements where D and E are not next to each other: 120 - 48 = 72 ways.

How Many Ways Can Five People, A, B, C, D