An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.
-In how many ways can the awards be presented so that Maria and Olivia will be next to each
Other?
A) 1,440
B) 1,680
C) 720
D) 1,220

Question

Quizplus · Accepted Answer

Maria and Olivia can be treated as a single unit, so there are 6 units to arrange (5 individuals + 1 pair). The number of ways to arrange 6 units is 6! = 720. Within their unit, Maria and Olivia can be arranged in 2! = 2 ways. Therefore, the total number of arrangements is 720 * 2 = 1,440.

An Order of Award Presentations Has Been Devised for Seven