How many 4 digits numbers can be formed from the digits 1 to 10 if not digit can be repeated.

Answer

To solve the problem of how many 4-digit numbers can be formed from the digits 1 to 10 without repeating any digit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total digits available**:
We have the digits from 1 to 10, which gives us a total of 10 digits.

2. **Determine the number of choices for each digit position**:
- For the **thousands place** (1st digit), we can choose any of the 10 digits. So, there are 10 options.
- For the **hundreds place** (2nd digit), since we cannot repeat the digit used in the thousands place, we have 9 remaining options.
- For the **tens place** (3rd digit), we cannot use the digits chosen for the thousands and hundreds places, leaving us with 8 options.
- For the **units place** (4th digit), we cannot use the digits chosen for the previous three places, which gives us 7 options.

3. **Calculate the total combinations**:
Using the fundamental principle of counting, we multiply the number of choices for each digit position:
\[ \text{Total combinations} = 10 \times 9 \times 8 \times 7 \]

4. **Perform the calculation**:
\[ 10 \times 9 = 90 \]
\[ 90 \times 8 = 720 \]
\[ 720 \times 7 = 5040 \]

5. **Conclusion**:
Therefore, the total number of 4-digit numbers that can be formed from the digits 1 to 10 without repeating any digit is **5040**.