# Circular permutation - Arranging 4 persons around a circular table where 8 seats are there.

Suppose 4 persons $A,B,C$ and $D$ sit around a round table with 8 seats. Rotation by 8,16,24,... seats defines same arrangement and other rotations gives different arrangements. Find the number of ways that these four people can be seated at the round table.

My solution:

Place one person in any seat; that is a reference seat.

Now 3 persons in 7 seats gives $7\times6\times5$ arrangements (if seats are not labeled)

or $8\times7\times6\times5$ (if seats are labeled)

Is this approach right?

• Your answers are correct. – N. F. Taussig Mar 12 '16 at 14:44

simply thinking your way. The chair can be anyone if the $8$ so its ${8\choose 1}$ so it should be $8.7.6.5=1680$ alternatively they are simple permutations so its just $8P4$ which yields the same answer.