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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.)

tertre  Feb 18, 2018
 #1
avatar+87334 
+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

 

 

cool cool cool

CPhill  Feb 18, 2018
 #2
avatar+2765 
+2

Amazing, CPhill! Great job!smiley

tertre  Feb 18, 2018

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