# If 2 people out of 7 refuse to sit next to each other in a row of 7 seats, how many ways are possible?

##### 1 Answer

Feb 24, 2018

#### Explanation:

The total number of ways in which

#7 * 6 * 5 * 4 * 3 * 2 * 1 = 7! = 5040#

To find the number of these ways that are unacceptable because they result in the particular pair being sat next to one another, we can think of seating

That can be done in

So the total number of acceptable arrangements is:

#7! - 2 * 6! = 5040 - 1440 = 3600#