Introduction:
When 6 boys sit in a round table, we need to find the number of ways in which two particular boys sit together. Let's solve this problem step by step.

Step 1: Fixing the position of the two boys sitting together:
Since the two particular boys need to sit together, we can consider them as a single unit. This means that we have 5 units (4 individual boys + 1 unit of two boys) to arrange around the table.

Step 2: Arranging the remaining boys:
Now, we need to arrange the remaining 4 individual boys around the table. Since it is a round table, the arrangement can be considered as a circular permutation.

Circular Permutation Formula:
The number of ways to arrange n objects in a circle is (n-1)!

Step 3: Calculating the number of arrangements:
Applying the circular permutation formula, we can calculate the number of ways to arrange the remaining 4 individual boys around the table as:

(4-1)! = 3!

Step 4: Calculating the total number of arrangements:
Now, we need to combine the two steps to calculate the total number of arrangements. Since the position of the two boys sitting together can be chosen in 2 ways (either on the left or right side), we multiply the number of arrangements from Step 2 by 2.

Total number of arrangements = 2 * 3! = 2 * 3 = 6

Conclusion:
There are 6 different ways in which 6 boys can sit in a round table so that two particular boys sit together.

5! - 4!2! = 120 - 48 = 72