If 3 sisters and 8 others girls, are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is 

The total number of ways that all girls seated around a circle is 10!
The number of ways the thre sisters seated together along with the other ggirls is 8! × 3!
So, required number fo ways
$\begin{array}{l}=10!-8!3!\\ =8!(10\times 9-6)=8!\times 84\end{array}$