There are 3 Americans, 2 British, 1 Chinese, 1 Dutch and 1 Egyptian. They are to be arranged around a circular table so that persons of same nationality are separated. (I found a similar thread on this site but wasn't able to get my answer since I am unable to form the case when ONLY two Americans are separated. Ways of arranging of different nationality persons at a round table )
I provide a startup for you.
Place an American.
Then $5$ spots are left for the other two Americans in the sense that they cannot be placed next to the one that has a seat already.
$\binom52$ ways to find $2$ out of $5$ but - because they cannot sit next to each other $4$ possibilities fall out. Next to that as human beings they are distinguishable so order matters here.
This gives $2\left(\binom52-4\right)=12$ possibilities.
These possibilities can be split in two specific configurations (make a picture to get view on this) of $6$.
Now start placing the $2$ British in both configurations.
I leave the rest to you.