SOLUTION: Twelve persons are to sit at a round table. Two particular people insist on sitting opposite each other. Find the number of ways the twelve can be seated.

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Question 934786: Twelve persons are to sit at a round table. Two particular people insist on sitting opposite each other. Find the number of ways the twelve can be seated.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the 2 people that want to be are seated
opposite each other, there are 2 ways to
to do this a opposite b, and then switch
seats, b opposite a
----------------------
They can do this for 6 seats to make all the
possibilities, so +2%2A6+=+12+ possible
----------------------
There are 10 seats left once they are seated,
and the possible seatings of 10 people is:
10%2A9+%2A8%2A7+%2A6+%2A5%2A4%2A3%2A2%2A1+
Factoring in the seatings for the opposite ones,
I get:
+12%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1+
You can do the math
Hope I got it