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

#2**+1 **

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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.

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