In how many ways can 7 women and 4 men be seated in a row of 11 seats at a movie theater assuming that allthe women must sit together and all the men must sit together?
A) 241,920
B) 120,960
C) 39,916,800
D) 2048

Question

Quizplus · Accepted Answer

The 7 women can be treated as a single unit and the 4 men as another unit. So, we have 2 units to arrange, which can be done in 2! ways. Within the women unit, the 7 women can be arranged in 7! ways, and within the men unit, the 4 men can be arranged in 4! ways. Therefore, the total number of arrangements is 2! * 7! * 4! = 2 * 5040 * 24 = 241,920.

In How Many Ways Can 7 Women and 4 Men