Ways to Arrange Seven Boys in a Round Table with Two Particular Boys Missing Together
There are a total of 7 boys that need to be arranged in a round table. We want to find the number of ways in which two particular boys, let's say A and B, are not seated together.

Calculate the Total Number of Ways
To calculate the total number of ways the boys can be arranged in a round table, we use the formula (n-1)!, where n is the total number of boys. In this case, n = 7, so the total number of ways is 6!.

Calculate the Number of Ways with A and B Together
If A and B are considered as one entity, then the total number of boys reduces to 6. Hence, the number of ways A and B can be arranged together is 5!.

Calculate the Number of Ways with A and B Not Together
To find the number of ways A and B are not together, we subtract the number of ways they are together from the total number of ways. Therefore, the number of ways A and B are not seated together is 6! - 5!.

Final Calculation
Calculating the values, we get:
Total number of ways = 6!
Number of ways with A and B together = 5!
Number of ways with A and B not together = 6! - 5!
Therefore, the number of ways in which seven boys can sit in a round table so that two particular boys (A and B) are not seated together is 6! - 5! = 600.