A meeting is held with eight people around a circular table. Two of the participants, April and May, want to sit that there is exactly one other person between them. How many different seatings are possible? (Two seatings are considered the same if one can be rotated to obtain the other.)

Forumofweb2.0cal Feb 18, 2020

#1**+1 **

There are 8 ways to choose where April and May sit. Then there are 6! ways to seat the remaining 6 people. We then divide by 8 to account for the rotation, so there are 8*6!/8 = 720 possible seatings.

Guest Feb 18, 2020

#3**+2 **

"Anchor" April and May in any two seats with a seat between them

We can seat them in 2 ways

For the person between them we have C (6,1) = 6 possibilities

And the other 5 people can be seated in 5! =120 ways

So.....the total possible arrangements =

2 * 6 * 120 =

12 * 120 =

1440

CPhill Feb 18, 2020