A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting a 4 digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock?

Options

A. `4^9`
B. `""^(9)P_4`
C. `9^4`
D. none of these

Answer

To solve the problem of how many different 4-digit codes can be formed using a letter lock that consists of 4 rings, each containing 9 non-zero digits, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a lock with 4 rings.
- Each ring can display one of 9 non-zero digits (1 through 9).

2. **Identifying Choices for Each Ring**:
- For each of the 4 rings, we can choose any of the 9 digits.
- This means for each ring, there are 9 possible choices.

3. **Calculating Total Combinations**:
- Since the choice for each ring is independent of the others, we multiply the number of choices for each ring together.
- Therefore, the total number of combinations can be calculated as:
\[ \text{Total Codes} = 9 \times 9 \times 9 \times 9 = 9^4 \]

4. **Final Calculation**:
- Calculate \(9^4\):
\[ 9^4 = 6561 \]

5. **Conclusion**:
- The maximum number of codes that can be formed to open the lock is **6561**.

### Final Answer:
The maximum number of codes that can be formed to open the lock is **6561**.

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