4 boys and 2 girls are to be seated in a row in such a way that the two girls are always together. In how many different ways can they be seated?

Options

A. 1200
B. 7200
C. 148
D. 240

Answer

To solve the problem of seating 4 boys and 2 girls in a row such that the two girls are always together, we can follow these steps:

### Step-by-Step Solution:

1. **Group the Girls Together**: Since the two girls must always sit together, we can treat them as a single unit or "block". This means we can consider the two girls as one entity.

- So, instead of having 4 boys and 2 girls, we now have 4 boys + 1 block of girls = 5 entities to arrange.

2. **Arrange the Entities**: We need to arrange these 5 entities (4 boys + 1 block of girls). The number of ways to arrange 5 entities is given by the factorial of the number of entities.

- The number of arrangements = 5! = 5 × 4 × 3 × 2 × 1 = 120.

3. **Arrange the Girls Within Their Block**: The two girls can be arranged among themselves in different ways. Since there are 2 girls, the number of ways to arrange them is given by 2!.

- The number of arrangements of the girls = 2! = 2 × 1 = 2.

4. **Calculate the Total Arrangements**: To find the total number of arrangements, we multiply the number of arrangements of the entities by the number of arrangements of the girls within their block.

- Total arrangements = (Number of arrangements of entities) × (Number of arrangements of girls)
- Total arrangements = 5! × 2! = 120 × 2 = 240.

### Final Answer:
The total number of different ways the 4 boys and 2 girls can be seated in a row, with the condition that the two girls are always together, is **240**.

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