For a group photograph, 3 boys and 2 girls stand in a line in all possible ways. How many photos could be taken if each photo corresponds to each such arrangement ?

Answer

To find the total number of arrangements for 3 boys and 2 girls standing in a line, we can follow these steps:

### Step 1: Determine the total number of individuals
We have a total of 3 boys and 2 girls, which sums up to:
\[ 3 + 2 = 5 \text{ individuals} \]

### Step 2: Calculate the number of arrangements
The number of ways to arrange \( n \) distinct objects in a line is given by \( n! \) (n factorial). In our case, we have 5 individuals, so we need to calculate \( 5! \):
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 3: Perform the multiplication
Now we can compute the factorial:
\[ 5! = 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]
\[ 60 \times 2 = 120 \]
\[ 120 \times 1 = 120 \]

### Step 4: Conclusion
Thus, the total number of different arrangements (or photos) that can be taken with 3 boys and 2 girls standing in a line is:
\[ \text{Total arrangements} = 120 \]

### Final Answer
The total number of photos that could be taken is **120**.

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