In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?

Question: In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?

Solution:
Total no. of unrestricted arrangements = (7 – 1)! = 6!
When two particular person always sit together, the total no. of arrangements = 6! - 2 × 5!
Required no. of arrangements = 6! - 2 × 5!
= 5! (6 - 2)
= 5 × 4 × 3 × 2 × 4
= 480