SOLUTION: how many ways can 8 people be seated at a round table if two people must not sit next to each other?

Algebra ->  Permutations -> SOLUTION: how many ways can 8 people be seated at a round table if two people must not sit next to each other?      Log On


   

Question 968536: how many ways can 8 people be seated at a round table if two people must not sit next to each other?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
7! = 5040 ways where anybody sits anywhere.

minus the number of ways the two sit side by side:

2 ways they can sit side by side, then
5! ways to arrange the other 5 around them.

7! - 2*5! = 5040 - 2(120) = 5040 - 240 = 4800 ways.

Edwin