Similar to your previous question.
Whatever place John or Sam are in, the other one must be in position #6 over from him.
let's line them up in a straight line,
the first spot can be filled in 2 ways, (John or Sam)
then the 6th spot can be filled in 1 way (one of John or Sam)
now fill in the other 8 places, so I see them lined up as follows:
2x8x7x6x5x1x4x3x2x1
= 80640
So when placing them around the table, we can consider the first spot to be any of on 10 places, so
number of ways 80640/10 = 8064
In how many ways can the 10 kids in my class be seated in a circle if John and Sam insist on being seated diametrically opposite each other?
(As usual, two seatings which are rotations of each other are considered the same.)
I do not understand this!
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