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How many ways can 10 people sit around a round table?

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

Exact result

362,880

10 distinct items around a circle can be arranged in 362,880 ways.

For 10 people around one round table, seatings that differ only by rotation are the same. Fix one seat, then arrange the remaining 9 people.

Worked steps

Show your work

  1. Input: n = 10
  2. Formula: (n - 1)!
  3. Substitute: (10 - 1)!
  4. Steps: fix one seat and arrange the remaining 9 items
  5. Result: 10 distinct items around a circle can be arranged in 362,880 ways.

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For 10 people around one round table, seatings that differ only by rotation are the same. Fix one seat, then arrange the remaining 9 people.

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