In how many different ways 5 girls can be seated in a row?

Answer

To find the number of different ways to seat 5 girls in a row, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Girls**: We have 5 girls who need to be seated.

2. **Determine the Number of Seats**: Since we are seating them in a row, we have 5 seats available.

3. **Calculate the Number of Ways to Fill Each Seat**:
- For the **1st seat**, any of the 5 girls can sit there. So, there are **5 options**.
- After seating one girl in the 1st seat, **4 girls** remain. For the **2nd seat**, there are **4 options**.
- After seating a girl in the 2nd seat, **3 girls** remain for the **3rd seat**, giving us **3 options**.
- For the **4th seat**, there will be **2 girls** left, which gives us **2 options**.
- Finally, for the **5th seat**, there will be only **1 girl** left, resulting in **1 option**.

4. **Multiply the Number of Options**: To find the total number of arrangements, we multiply the number of options for each seat:
\[ 5 \times 4 \times 3 \times 2 \times 1 \]

5. **Calculate the Result**:
\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]
\[ 60 \times 2 = 120 \]
\[ 120 \times 1 = 120 \]

6. **Final Result**: Therefore, the total number of different ways to seat 5 girls in a row is **120**.

Alternatively, we can express this using factorial notation:
\[ 5! = 120 \]