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How many ways can 9 people sit around a round table?

This is a circular permutation because the relative order around the table matters, but rotating the whole seating does not create a new arrangement.

Exact result

40,320

9 distinct items around a circle can be arranged in 40,320 ways.

For 9 people around one round table, seatings that differ only by rotation are the same. Fix one seat, then arrange the other 8 people.

Worked steps

Show your work

  1. Input: n = 9
  2. Formula: (n - 1)!
  3. Substitute: (9 - 1)!
  4. Steps: fix one seat and arrange the remaining 8 items
  5. Result: 9 distinct items around a circle can be arranged in 40,320 ways.

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For 9 people around one round table, seatings that differ only by rotation are the same. Fix one seat, then arrange the other 8 people.

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