Problem Statement: The number of ways in which 7 boys sit in a round table so that two particular boys may sit together?

Solution:
To solve this problem, we need to use the concept of circular permutations and arrangement.

Step 1: Total number of ways the 7 boys can sit in a round table
The total number of ways in which 7 boys can sit in a round table is given by circular permutation formula:
n!/(n-r)!
where n is the total number of objects (boys) and r is the number of objects (boys) selected.

Thus, the total number of ways the 7 boys can sit in a round table is:
7!/7! = 1

Step 2: Two particular boys sit together
Let's assume that the two particular boys who need to sit together are A and B. Now we can consider them as a single unit. So we have 6 units (including AB) to arrange on the round table.

Step 3: Total number of ways 6 units can sit in a round table
The total number of ways in which 6 units can sit in a round table is given by circular permutation formula:
n!/(n-r)!
where n is the total number of objects (units) and r is the number of objects (units) selected.

Thus, the total number of ways the 6 units can sit in a round table is:
6!/6! = 1

Step 4: Total number of ways A and B can sit within their unit
Since A and B can sit in any of the 2 positions within their unit, there are 2 ways in which they can sit.

Step 5: Total number of ways 7 boys can sit in a round table such that A and B sit together
The total number of ways in which 7 boys can sit in a round table such that A and B sit together is given by the product of the total number of ways the 6 units can sit in a round table and the total number of ways A and B can sit within their unit:
1 * 2 = 2

Therefore, there are 2 ways in which 7 boys can sit in a round table such that A and B sit together.

5! × 2! = 240