@amusingminnow Hi Edward, thanks so much for writing. Since you are asking about an exam question, we'll answer over email instead of here on the forum, just to keep the exam questions private. Thanks for understanding!
@spaceblastxy1428 Hi there, since this doesn't give away the solution, I'll answer here. The question was written with the intention of not having rotational symmetry. Pretend the chairs are numbered from \(1\) to \(6,\) so that if you rotate a seating arrangement, then it's considered a new arrangement. We can clarify this in the question statement. Thanks for asking!