Without repeating any digit, the sum of all digits of the greatest ten digit number is

Options

A. 45
B. 44
C. 42
D. 39

Answer

To solve the problem of finding the sum of all digits of the greatest ten-digit number without repeating any digit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The digits available to us are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. There are a total of 10 digits.

2. **Form the Greatest Ten-Digit Number**: To create the greatest ten-digit number, we need to arrange these digits in descending order. The greatest number we can form using all the digits without repeating any is:
\[ 9876543210 \]

3. **Sum the Digits**: Now, we need to find the sum of all the digits in the number 9876543210. We can do this by adding each digit together:
\[ 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 \]

4. **Perform the Addition**:
- First, add the largest pairs:
- \(9 + 8 = 17\)
- \(17 + 7 = 24\)
- \(24 + 6 = 30\)
- \(30 + 5 = 35\)
- \(35 + 4 = 39\)
- \(39 + 3 = 42\)
- \(42 + 2 = 44\)
- \(44 + 1 = 45\)
- \(45 + 0 = 45\)

5. **Final Result**: The sum of all the digits is:
\[ 45 \]

### Conclusion:
The sum of all digits of the greatest ten-digit number without repeating any digit is **45**.

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