Question

Assume that four men and four women are to sit in a row of eight chairs. In how many ways can these people sit if all men must sit together and all the women must sit​ together? Use the fundamental counting principle. To apply this​ principle, first identify the separate tasks involved in making the seating arrangements.

Answer 1

Answer:

The people can sit in 1,152 possible ways if all men must sit together and all women must sit​ together.

Explanation:

The 4 men must sit together.

Number of ways to arrange the 4 men together

= 4! = 4 x 3 x 2 x 1 = 24

Similarly, the 4 women must sit together.

Number of ways to arrange the 4 women together

= 4! = 4 x 3 x 2 x 1 = 24

Now the 8 chairs are placed in a row. There are 2 ways to arrange the men and women: either the men must sit in the first 4 chairs and women in the last 4 chairs, or the women must sit in the first 4 chairs and men in the last 4 chairs.

Hence, total number of ways to arrange the 8 people

= 24 x 24 x 2

= 1,152