How many codes containing 3 letters can be formed with the 9 letters of English alphabet if repetition is not allowed?

Answer

To find the number of codes containing 3 letters that can be formed with 9 letters of the English alphabet without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of letters available**:
We have 9 unique letters.

2. **Determine the number of choices for the first letter**:
For the first letter of the code, we can choose any of the 9 letters.
- Choices for the first letter = 9

3. **Determine the number of choices for the second letter**:
Since repetition is not allowed, after choosing the first letter, we have 8 letters left to choose from for the second letter.
- Choices for the second letter = 8

4. **Determine the number of choices for the third letter**:
After choosing the first and second letters, we have 7 letters remaining for the third letter.
- Choices for the third letter = 7

5. **Calculate the total number of codes**:
To find the total number of different codes that can be formed, we multiply the number of choices for each letter together:
\[ \text{Total Codes} = \text{Choices for first letter} \times \text{Choices for second letter} \times \text{Choices for third letter} \]
\[ \text{Total Codes} = 9 \times 8 \times 7 \]

6. **Perform the multiplication**:
\[ 9 \times 8 = 72 \]
\[ 72 \times 7 = 504 \]

7. **Conclusion**:
Therefore, the total number of codes that can be formed is **504**.