A Round Table Probability Question

Question

Mr. Blue, Mr. Black, Mr. Green, Mrs. White, Mrs. Yellow and Mrs. Red sit around a circular table. Calculate the number of different ways that these six people can sit at the table in such a way that Mr. Black and Mrs. White do not sit together.

Answer

In a circular arrangement, the number of ways one can permutate n objects in a circle is (n-1)!

Thus if there were no restrictions, answer would be
(6-1)! = 5! = 5 x 4 x 3 x 2 x 1 = 120 ways
Of these 120 ‘ways’, how many has Mr.Black and Mrs.White sit together? Treat this new problem with ‘MrBlack & Mrs White’ as ‘one object. So we have ‘5’ objects and we can permutate these in (5 – 1)! ways = 4! = 24 ways.
Hence, the number of ways Mr Black and Mrs White don’t sit together is = 120 – 24 = 96 ways.