Solution
The Round Table
Show the problem again
In how many distinct ways can 8 people be seated around a circular table, where two seatings are considered the same if one is a rotation of the other?
Worked solution
The answer is 5040. Fix one person's seat to kill the rotational symmetry; the remaining 7 people can be arranged in the other seats in 7! = 5040 ways. Equivalently, 8!/8 = 7!, since each circular arrangement corresponds to 8 rotations of a linear one.
Source: Standard circular-permutation exercise from introductory combinatorics texts. Statement written for AxiomIQ.