Exercise 871Combinatorics › Counting principlesL1Added 3 Nov 2026

Circular arrangements

#circular permutations#necklace#seating

Statement

In how many ways can $6$ people sit around a round table (rotations considered the same)?

Hint

Fix one person to break the rotational symmetry; then arrange the rest.

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Fix one. Place person $1$ at a reference seat. The remaining $5$ people can be arranged in $5!=120$ ways.

Conclusion. There are $120$ circular arrangements.

Formula. For $n$ people, $(n-1)!$ circular permutations.