How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?

Options

A. 3024
B. 3000
C. 9*9*9
D. None of these

Explanation

To find how many 4-digit numbers can be formed using the digits 1 to 9 without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits Available**: The digits available are 1, 2, 3, 4, 5, 6, 7, 8, and 9. This gives us a total of 9 different digits.

2. **Determine the Number of Positions**: We need to form a 4-digit number, which means we have 4 positions to fill.

3. **Select a Digit for the First Position**:
- For the first digit, we can choose any of the 9 digits (1 to 9).
- **Choices for the first position**: 9

4. **Select a Digit for the Second Position**:
- After choosing the first digit, we cannot use it again (since repetition is not allowed).
- This leaves us with 8 remaining digits.
- **Choices for the second position**: 8

5. **Select a Digit for the Third Position**:
- After filling the first and second positions, we have used 2 digits, leaving us with 7 digits available.
- **Choices for the third position**: 7

6. **Select a Digit for the Fourth Position**:
- After filling the first three positions, we have used 3 digits, leaving us with 6 digits available.
- **Choices for the fourth position**: 6

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

8. **Perform the Calculation**:
- Calculate \(9 \times 8 = 72\)
- Then \(72 \times 7 = 504\)
- Finally, \(504 \times 6 = 3024\)

### Final Answer:
The total number of 4-digit numbers that can be formed using the digits 1 to 9 without repetition is **3024**.

---