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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.)

 Feb 18, 2018

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



cool cool cool

 Feb 18, 2018

Amazing, CPhill! Great job!smiley

tertre  Feb 18, 2018

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