now, if every member is playing the other 7, that means each game will have two players, so, seems to me is, how many Permutations of 2 from a group of 8?
[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\quad
\begin{cases}
n=8\\
r=2
\end{cases}\implies _8P_2=\cfrac{8!}{(8-2)!}[/tex]
