The number of ways in which 10 boys can take positions around a circular round table, if two particular boys must not be seated side by side, is

Total number of ways without any restriction = 9!
 Considering two of the particular boys sit together and then assuming them as one, the total no. of ways = 8!
They themselves can be arranged in 2 ways.
So, the required number of ways
$=9!-2\times 8!=7\times 8!$