What is the sum of all the possible three - digit number that can be constructed using the digits 3,4, and 5 if each digit can be used only in each number?

Options

A. 1440
B. 3125
C. 2664
D. 1028

Answer

To find the sum of all the possible three-digit numbers that can be constructed using the digits 3, 4, and 5, where each digit can only be used once in each number, we can follow these steps:

### Step 1: Identify all possible three-digit combinations
We can form three-digit numbers using the digits 3, 4, and 5. Since we are using each digit exactly once, we can list all the permutations of these digits.

The possible three-digit numbers are:
1. 345
2. 354
3. 435
4. 453
5. 534
6. 543

### Step 2: Calculate the sum of these numbers
Now we will add all these numbers together:

- 345
- 354
- 435
- 453
- 534
- 543

Let's perform the addition step by step:

1. **Add 345 and 354:**
\[ 345 + 354 = 699 \]

2. **Add the result to 435:**
\[ 699 + 435 = 1134 \]

3. **Add the result to 453:**
\[ 1134 + 453 = 1587 \]

4. **Add the result to 534:**
\[ 1587 + 534 = 2121 \]

5. **Finally, add the result to 543:**
\[ 2121 + 543 = 2664 \]

### Step 3: Conclusion
The sum of all the possible three-digit numbers that can be constructed using the digits 3, 4, and 5 is **2664**.