The number of ways, in which 6 boys and 5 girls can sit at a round table, if no two girls are to sit together, is

Step-by-step solution

With 6 distinguishable boys, the number of distinct circular arrangements is (6-1)! = 5! = 120 . These boys create 6 distinct spaces for seating the 5 distinguishable girls, ensuring no two girls are adjacent. The number of ways to choose 5 of the 6 spaces is C(6,5) = 6 . The number of ways to arrange the 5 girls among the chosen spaces is 5! = 120 . The total number of seating arrangements is the product: 5! C(6,5) 5! = 120 6 120 = 86400 .