Question

8 people are going to sit on 6 chairs. Two of them John and Kelly can't sit next to each other. How many ways can you put the people to seats?
The answer is 10080, but I can't figure out how to calculate it.

Answer 1

There are 8 people in total and six places so use the formula n!/(n-r)! but two people cannot be next to each other thus the end formula will look like this:
n!/2(n-r)!
= 8!/2(8-6)!
= 10080