In how many ways can 6 boys be arranged at a round table so that 2 particular boys may be together ?

Options

A. a. 24
B. b. 48
C. c. 360
D. d. 60

Answer

To solve the problem of arranging 6 boys at a round table such that 2 particular boys are always together, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Arrangement**:
When arranging objects in a circle, the formula to calculate the number of arrangements is (n - 1)!, where n is the number of objects. Here, we have 6 boys.

2. **Grouping the Two Particular Boys**:
Since we want the two particular boys (let's call them Boy A and Boy B) to sit together, we can treat them as a single unit or group. This means instead of 6 individual boys, we now have 5 units to arrange: the group (AB) and the other 4 boys (C, D, E, F).

3. **Calculating the Arrangements of the Groups**:
Now, we need to arrange these 5 units around the round table. Using the formula for circular arrangements, we have:
\[ \text{Arrangements} = (5 - 1)! = 4! = 24 \]

4. **Arranging the Boys within the Group**:
Within the group (AB), Boy A and Boy B can be arranged in 2 different ways (AB or BA). Therefore, we multiply the arrangements of the groups by the arrangements within the group:
\[ \text{Total Arrangements} = 4! \times 2! = 24 \times 2 = 48 \]

5. **Final Answer**:
Thus, the total number of ways to arrange the 6 boys at a round table such that the two particular boys are together is **48**.