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

(A)  7! 

(B)  5 x 6!

(C)  6 x 6! 

(D)  5 x 7!

Answer 1

Correct option (B) 5 × 6! 

The 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 way of arranging those people, where B₁ and G₁ are always together. When B₁ & G₁ are together, we get 

4 Boys + 2 Girls + 1(B₁ + G₁) 

That is, 7 people and since B₁ + G₁ be permitted in 2 ways, those can be arranged in 6! x 2 ways. 

Subtracting, we have the required number of ways as follows: 

7! - 6! x 2 = 6!(7 - 2) =5 x 6! ways.