In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?

There are 1152 ways to seat 8 people such that no two men or women are sitting together.

Step-by-step 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.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is