G4.4 $A, B, C, D, E, F, G$ are seven people sitting around a circular table. If $d$ is the total number of ways that $B$ and $G$ must sit next to $C$, find the value of $d$.
If $B, C, G$ are neighbours, we can consider these persons bound together as one person. So, there are 5 persons sitting around a round table. The number of ways should be 5 !. Since it is a round table, every seat can be counted as the first one. That is, $A B C D E$ is the same as $B C D E A, C D E A B, D E A B C, E A B C D$. Therefore every 5 arrangements are the same. The number of arrangement should be $5!\div 5=4!=24$. But $B$ and $G$ can exchange their seats.
$\therefore$ Total number of arrangements $=24 \times 2=48$.