4 boys and three girls are to be seated in a row in such way that no two boys sit adjacent to each other in how many different ways can it be done?

Options

A. 5040
B. 30
C. 144
D. 72

Answer

To solve the problem of seating 4 boys and 3 girls in a row such that no two boys sit adjacent to each other, we can follow these steps:

### Step 1: Arrange the Girls
First, we will arrange the 3 girls. The number of ways to arrange 3 girls is given by the factorial of the number of girls:

\[ \text{Ways to arrange girls} = 3! = 6 \]

### Step 2: Identify the Gaps for Boys
Once the girls are arranged, they create gaps where the boys can sit. For 3 girls, the arrangement will look like this:

- G G G

This arrangement creates 4 gaps (before the first girl, between the girls, and after the last girl):

- _ G _ G _ G _

Thus, we have 4 gaps available for the boys.

### Step 3: Place the Boys in the Gaps
Since we have 4 boys and 4 gaps, we can place one boy in each gap. The number of ways to arrange 4 boys in these 4 gaps is given by the factorial of the number of boys:

\[ \text{Ways to arrange boys} = 4! = 24 \]

### Step 4: Calculate the Total Arrangements
Now, we can find the total number of arrangements by multiplying the number of ways to arrange the girls by the number of ways to arrange the boys:

\[ \text{Total arrangements} = \text{Ways to arrange girls} \times \text{Ways to arrange boys} = 3! \times 4! = 6 \times 24 = 144 \]

### Final Answer
Thus, the total number of ways to seat 4 boys and 3 girls in a row such that no two boys sit adjacent to each other is:

\[ \boxed{144} \]