The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is

Step-by-step solution

Circular arrangements with restrictions are computed using complementary counting. The total arrangements of 10 distinct people around a circular table is (10-1)! = 9! . To count arrangements where two special boys and one special girl always sit together, treat them as a single block. Within this block, they can be arranged in 3! ways. With the block considered as one entity, there remain 7 people, giving (8-1)! = 7! circular arrangements. The number of restricted arrangements is therefore 3! 7! . The number of va