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Seating six people around a round table

countingpermutationscircularsymmetry

Six people sit around a round table. Two seatings count as the same if one is a rotation of the other, since all that matters is who is next to whom (and on which side).

  1. How many different seatings are there?
  2. How many if seatings that are mirror images are also counted as the same (so only "who is beside whom" matters, not left versus right)?
  3. How many if two particular people insist on sitting together?
Show a hint

Fix one person's seat to kill the rotations, then arrange the others.

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