Answer:
There are 1152 ways to seat 8 people such that no two men or women are sitting together.
Explanation:
In a group of 8 people there are 4 men and 4 women.
These 8 people are to seated in a row such that no 2 men or 2 women can sit next to each other.
That is, men and women are sitting alternatively.
M, W, M, W, M, W, M, W
This can happen in 2 ways because the first place can be occupied by a women.
Compute the number of ways of seating 8 people as follows:
The 4 men can sit in 4! ways.
The 4 women can sit in 4! ways.
The number of ways is: 4! × 4! × 2 = 1152
Thus, there are 1152 ways to seat 8 people such that no two men or women are sitting together.