How many four digit numbers formed by the digits {1,2,3,….9} if repetition of digits is not allowed

Answer

To solve the problem of how many four-digit numbers can be formed using the digits {1, 2, 3, ..., 9} without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to form a four-digit number using the digits from 1 to 9. Since repetition of digits is not allowed, each digit can only be used once in each number.

2. **Choosing the First Digit**: The first digit of a four-digit number cannot be 0 (but since we are only using digits from 1 to 9, this is not an issue). We can choose any of the 9 digits (1 through 9) for the first position.
- **Choices for the first digit**: 9 options.

3. **Choosing the Second Digit**: After selecting the first digit, we have 8 remaining digits to choose from for the second position.
- **Choices for the second digit**: 8 options.

4. **Choosing the Third Digit**: After selecting the first and second digits, we have 7 remaining digits to choose from for the third position.
- **Choices for the third digit**: 7 options.

5. **Choosing the Fourth Digit**: After selecting the first three digits, we have 6 remaining digits to choose from for the fourth position.
- **Choices for the fourth digit**: 6 options.

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

7. **Performing the Calculation**:
- Calculate \(9 \times 8 = 72\)
- Calculate \(72 \times 7 = 504\)
- Calculate \(504 \times 6 = 3024\)

8. **Final Answer**: Therefore, the total number of four-digit numbers that can be formed using the digits {1, 2, 3, ..., 9} without repetition is **3024**.