How many 9- digits numbers of different digits can be formed?

Answer

To solve the problem of how many 9-digit numbers with different digits can be formed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the First Digit**:
- A 9-digit number cannot start with the digit '0'. Therefore, the first digit can be any digit from 1 to 9.
- This gives us 9 options for the first digit.

2. **Identify the Second Digit**:
- The second digit can be any digit from 0 to 9, but it must be different from the first digit.
- Since we have already used one digit (the first digit), we have 9 remaining choices (including '0') for the second digit.

3. **Identify the Third Digit**:
- The third digit must also be different from the first two digits.
- Thus, we have 8 choices left for the third digit.

4. **Continue for Remaining Digits**:
- Following the same logic:
- For the fourth digit: 7 choices remain.
- For the fifth digit: 6 choices remain.
- For the sixth digit: 5 choices remain.
- For the seventh digit: 4 choices remain.
- For the eighth digit: 3 choices remain.
- For the ninth digit: 2 choices remain.

5. **Calculate the Total Number of Combinations**:
- To find the total number of different 9-digit numbers, we multiply the number of choices for each digit:
\[ \text{Total} = 9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \]

6. **Perform the Calculation**:
- Now, we can calculate the total:
\[ 9 \times 9 = 81 \]
\[ 81 \times 8 = 648 \]
\[ 648 \times 7 = 4536 \]
\[ 4536 \times 6 = 27216 \]
\[ 27216 \times 5 = 136080 \]
\[ 136080 \times 4 = 544320 \]
\[ 544320 \times 3 = 1632960 \]
\[ 1632960 \times 2 = 3265920 \]

Thus, the total number of different 9-digit numbers that can be formed is **3,265,920**.

### Final Answer:
**3,265,920**