Round Table Seating

Fix one person's seat to remove rotational symmetry.

Arrange the remaining 7 people in the remaining seats.

1. 1. Fix a reference

   Fix one person's position to account for rotational equivalence.

2. 2. Arrange the rest

   The remaining 7 people can be arranged in $7!$ ways.

   $$7!=5040$$

Answer: 7!