Question

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B₁ and a particular girl G₁ never sit adjacent to each other, is.

Answer 1

Number of ways of arranging 5 boys and 3 girls, i.e. 8 people on a round table would be 7!

We subtract the number of ways of arranging those people when B₁ and G₁ are always together to get the required answer.

When B₁ and G₁ are together, we get 4 boys +2 girls + 1(B₁ + G₁) i.e. 7 people and since B₁+G₁ can be permuted in 2 ways, these can be arranged in 6! x 2 ways.

Subtracting, we have 7! - 6! x 2 =6!(7−2)

=5×6! ways in total.