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How many ways are there for 8 people to sit around a circular table if none of Alice, Bob, and Eve (three of the 8 people) want to sit next to each other? Two seatings are considered the same if one is a rotation of the other.

Guest Mar 20, 2018
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Bump, so that someone can answer this

Guest Mar 20, 2018
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If you have already asked this question then you should include a link to the original question and ask people to answer it on the original. Otherwise you may get two answers and this annoys answerers. 

 

How many ways are there for 8 people to sit around a circular table if none of Alice, Bob, and Eve (three of the 8 people) want to sit next to each other? Two seatings are considered the same if one is a rotation of the other.

 

Anyway, I'd just seat the 5 first.  Sit one anywhere and then there are 4! = 24 ways to seat the others.

 

Now we have 5 between spots where we can sit the other 3 people.  So that woud be 5P3 = 60 ways

 

So that is  24*60 = 1440 ways I think. 

Melody  Mar 20, 2018

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