Official solution
Number of ways = Total - when B1 and G1 sit together
Total ways to seat 8 people on round table = (8 - 1)! = 7!
When B1 and G1 sit together then assume B1 and G1 are one people, so total 7 people are there and among B1 and G1 they can sit 2! ways.
So total no of ways when B1 and G1 sit together
= (7 - 1)! \[ \times \] 2! = 6! \[ \times \] 2!
Number of ways = 7! - 6! \[ \times \] 2! = 6!\[ \times (7 - 2) = 5 \[ \times \] 6!