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How many ways in a round table 8 boys can sit....
1)If, Ron and Harry sit opposite site of the table?
2)Snape and Molfoy can't sit side by side?

Let's label the chairs with $0,1,2,3,4,5,6,7$.
Start by placing Ron at position $0$ and Harry at position $4$.

If we put Snape at either of this positions : $1,3,5,7$, then there will be $4$ seats left for molfoy to sit.
If we let Snape seat at these positions : $2,6$, then there will be $3$ seats left for Molfoy to seat.

So, there are $4\times4+2\times3=22$ arrangements for Snape and Molfoy.

There are $4!$ arrangements for the rest of the boys for each arrangement of Snape and Molfoy.

So, total number of arrangements $=4!\times22=24\times22=\boxed{528}$.

Use this kind of illustrations to investigate the cases of the problem :