In how many ways can we seat 8 people around a table if Alice and Bob won't sit next to each other? (Two seatings are the same if one is a rotation of the other.)

tertre
Feb 18, 2018

#1**+2 **

Anchor Alice in any position

And Bob can sit in any position except Alice's and the two positions on either side of her...so this gives 5 possible positions for him.....and for each of these, the other 6 people can be seated in 6! = 720 ways

So....the total arrangements are 5 * 6! = 5 * 720 = 3600 ways

CPhill
Feb 18, 2018