Seat 8 Guests Around a Round Table

Decision guide

Why this formula fits

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

Does order matter? Relative order matters, but a full rotation of the same seating is still the same circular arrangement.

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

Worked solution

8 distinct items around a circle can be arranged in 5,040 ways.

1. Input: n = 8
2. Formula: (n - 1)!
3. Substitute: (8 - 1)!
4. Steps: fix one seat and arrange the remaining 7 items
5. Result: 8 distinct items around a circle can be arranged in 5,040 ways.