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There is a square table and 2 persons are sitting on each side of it so there are 8 persons in total ... how many total number of permutation is possible?

Does circular permutation rules applies here?

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Why wouldn't it? – Kopper Mar 2 '11 at 16:06
@ Jay Kopper:Thanks :-) – VelvetThunder Mar 2 '11 at 16:08
Well, they sort of do: rotation by 1 person results in a different seating arrangement, so only rotations by an even displacement corresponds to the "same" seating. – Arturo Magidin Mar 2 '11 at 16:59

It depends on your definition of what sitting positions are to be considered different:

  • If chairs are considered all distict, the answer is obviously 8!=40320
  • If only the sequence of neighbours matters (that is, if rotations of chairs does not matter), (but clock and counter clock wise are considered different) we have a circular permutation: 7!=5040
  • If only 90 degrees rotations of the table induce equivalent arrangements (the most reasonable definition here, I'd say) one has 2 7! = 10080
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