Question

You have 9 chairs arranged in a circle, and wish to seat 9 people (one person per seat). The one constraint is that person A cannot sit next to person B or person C (three of the people). How many ways are there to seat them?

Answer 1

30240 number of ways are there to seat them

Explanation:

Total number of ways of arranging 9 people on 9 chairs in circular manners = (9-1)! = 8! =

number of ways A sit always sit next to B = AB together makes a single and

therefore total number of arrangements for this = 7+(AB) = 8 that is 8 persons sitting in circular manner

number of ways = (8-1)! =7! = 5040

likewise number of arrangements for A and C will be = 5040

Total number of ways such that A cannot sit next to B or C = total ways of 9 persons - total number of A always sitting next to B - total number of ways always sitting next to C = 8! - 7!-7!

= 40320- 5040-5040

= 30240

=