Question

In how many ways can 8 persons be seated at a round table if 2 particular persons must not sit next to each other?

• A. 40320
• B. 5040
• C. 3600
• D. 720

Answer 1

The correct option is C 3600

The no. of circular arrangements of n distinct items = (n-1)!
If A,B,C,D,E,F,G and H are the 8 persons to be seated around the table and A,B the 2
particular persons who must not sit together. Then,

The total no. of circular arrangements for 8 persons = (8-1)! = 7! = 5040 ---> (1)
The no. of circular arrangements possible if A and B were to sit together = 6! (considering A and B as a single pair).
But, A and B can interchange their positions.
Hence, the no. of arrangements $=6!\times 2=720\times 2=1440---->\left(2\right)$
So, the total number of arrangements possible if A and B must not sit together, = (1) - (2)
= 5040-1440
= 3600