Determine the Appropriate Counting Technique to Use
-In how many ways can 6 women and 4 men be seated in a row of 10 seats at a movie theater assuming that all the women must sit together and all the men must sit together
A) 34,560
B) 17,280
C) 3,628,800
D) 1024

Question

Quizplus · Accepted Answer

First, group all women together as a single unit and all men together as another unit, making 2 units in total. These 2 units can be arranged in 2! ways. Within the women's group, the 6 women can be arranged in 6! ways, and the 4 men can be arranged in 4! ways. Therefore, the total number of arrangements is 2! * 6! * 4! = 2 * 720 * 24 = 34,560.