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.