How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?
A) 18
B) 6
C) 24
D) 12

Question

Quizplus · Accepted Answer

Since Andy and Betty must sit together, we can treat them as a single entity, leaving us with three entities to arrange (Andy-Betty, Cindy, Doug). There are 3! = 6 ways to arrange these entities. However, within the Andy-Betty pair, there are 2! = 2 ways to arrange Andy and Betty. Therefore, the total number of arrangements is 3! * 2! = 6 * 2 = 12.

How Many Different Ways Can Four People: Andy, Betty, Cindy