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Problems Problem

Seat 7 Guests Around a Round Table

Seven guests are sitting around one round dinner table. How many distinct seatings are possible if rotations count as the same seating?

Decision guide

Why this formula fits

This is a circular permutation problem because rotating the full table does not create a new arrangement.

Does order matter? Relative order matters, but a full rotation of the same seating is not new.

Is repetition allowed? Repetition is not allowed because each guest occupies one seat exactly once.

Worked solution

7 distinct items around a circle can be arranged in 720 ways.

  1. Input: n = 7
  2. Formula: (n - 1)!
  3. Substitute: (7 - 1)!
  4. Steps: fix one seat and arrange the remaining 6 items
  5. Result: 7 distinct items around a circle can be arranged in 720 ways.

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This is a circular permutation problem because rotating the full table does not create a new arrangement.

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