Problem
COM-B1-M02-P016 Not Neighbors Around a Circle
#16
★★★☆☆ Level 3 of 5
In how many ways can \(8\) people sit at a round table if two specified people must not sit together?
Total circular seatings minus those where they are adjacent.
Total: \((8-1)!=5040\). If the two are adjacent, glue them into a block: \(7\) objects around a circle, \((7-1)!=720\), and \(2\) internal orders. Bad cases: \(1440\). Answer: \(5040-1440=3600\).
Combines circle and complement.