Three couples attend a dinner. No couple sits next to each other at a round table with 6 seats. How many seating arrangements exist? (Rotations identical.)

✓ Correct Answer: Option A

Fix one person. Total arrangements of remaining 5 = 5! = 120. Subtract those where at least one couple is adjacent. By inclusion-exclusion for derangement of couples at a round table: the answer is 12 valid arrangements.