Solve the problem.
-Amy has 5 blue, 3 red, and 4 green books to arrange on a shelf. In how many ways can the books be arranged if books of the same color must be grouped together? (Assume that books of the same color are distinguishable.)
A) 6
B) 150
C) 103,680
D) 17,280

Question

Quizplus · Accepted Answer

First, treat each color group as a single unit. There are 3 groups (blue, red, green), which can be arranged in 3! ways. Within each group, the books can be arranged among themselves: 5! for blue, 3! for red, and 4! for green. The total number of arrangements is 3! * 5! * 3! * 4! = 6 * 120 * 6 * 24 = 103,680.

Solve the Problem. -Amy Has 5 Blue, 3 Red, and 4 Green Books