What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed ?

Options

A. 2664
B. 3882
C. 4044
D. 4444

Explanation

To find the sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition, we can follow these steps:

### Step 1: Determine the total number of three-digit combinations
Since we have three distinct digits (3, 4, and 5), we can calculate the total number of three-digit numbers that can be formed using these digits without repetition. The formula for the number of permutations of n distinct objects taken r at a time is given by n!/(n-r)!.

Here, n = 3 (the digits 3, 4, and 5) and r = 3 (we want to form three-digit numbers).

\[ \text{Total combinations} = 3! = 6 \]

### Step 2: List all possible three-digit numbers
The six three-digit numbers that can be formed are:
1. 345
2. 354
3. 435
4. 453
5. 534
6. 543

### Step 3: Calculate the sum of these numbers
Now we will add these numbers together:

\[ 345 + 354 + 435 + 453 + 534 + 543 \]

Calculating step by step:
- \(345 + 354 = 699\)
- \(699 + 435 = 1134\)
- \(1134 + 453 = 1587\)
- \(1587 + 534 = 2121\)
- \(2121 + 543 = 2664\)

So, the total sum of all the three-digit numbers is:

\[ \text{Sum} = 2664 \]

### Final Answer
The sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition is **2664**.

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