Solve the problem.
-Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if no couple is to be separated?
A)24
B)192
C)40,320
D)384

Question

Quizplus · Accepted Answer

First, treat each couple as a single unit, which gives us 4 units (couples) to arrange in a row. This can be done in 4! = 24 ways. However, within each couple, there are 2 ways to arrange the two individuals (either person can sit on the left or the right). Since there are 4 couples, this gives us an additional 2^4 = 16 ways. Multiplying these together gives us 24 * 16 = 384 ways in total.

Solve the Problem. -Four Married Couples Have Reserved Eight Seats in a Row