Total number of ways in which 4 boys and 4 girls can be seated around a round table, so that no two girls sit together, is equal to.

Options

A. 7!
B. `(3!)(4)!`
C. `(4!)(4!)`
D. `(3!)(3!)`

Answer

To solve the problem of seating 4 boys and 4 girls around a round table such that no two girls sit together, we can follow these steps:

### Step-by-Step Solution:

1. **Arrange the Boys**:
Since the arrangement is around a round table, we can fix one boy to eliminate the effect of rotations. The remaining 3 boys can then be arranged in the remaining seats.
- The number of ways to arrange 4 boys in a round table is given by (n-1)! where n is the number of boys.
- Therefore, the number of arrangements for the boys is:
\[ (4-1)! = 3! = 6 \]

2. **Identify the Spaces for Girls**:
After seating the boys, there will be 4 gaps created between them where the girls can be seated. These gaps are:
- Gap 1: Between Boy 1 and Boy 2
- Gap 2: Between Boy 2 and Boy 3
- Gap 3: Between Boy 3 and Boy 4
- Gap 4: Between Boy 4 and Boy 1

3. **Arrange the Girls**:
Now, we need to place the 4 girls in these 4 gaps. Since we want to ensure that no two girls sit together, we can place one girl in each gap.
- The number of ways to arrange 4 girls in 4 gaps is given by 4! (factorial of the number of girls).
- Therefore, the number of arrangements for the girls is:
\[ 4! = 24 \]

4. **Calculate the Total Arrangements**:
To find the total number of arrangements where no two girls sit together, we multiply the number of arrangements of boys by the number of arrangements of girls:
\[ \text{Total arrangements} = \text{Arrangements of boys} \times \text{Arrangements of girls} = 6 \times 24 = 144 \]

### Final Answer:
The total number of ways in which 4 boys and 4 girls can be seated around a round table, so that no two girls sit together, is **144**.