A letter look consists of three rings marked with 15 different letters. If N denotes the number of ways in which it is possibel to make unsuccessful attempts to open lock, then

Options

A. 482 divides N
B. N product of 3 distint prime no.
C. N is product of 4 distinct prime no.
D. None of these

Answer

To solve the problem of determining the number of unsuccessful attempts to open a lock consisting of three rings marked with 15 different letters, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Lock Configuration**:
- The lock has 3 rings.
- Each ring can be filled with any of the 15 different letters.

2. **Calculating Total Possible Combinations**:
- Since each ring can have any of the 15 letters and repetitions are allowed, the total number of combinations can be calculated using the formula:
\[ \text{Total Combinations} = (\text{Number of Choices})^{\text{Number of Rings}} = 15^3 \]
- Calculate \(15^3\):
\[ 15^3 = 15 \times 15 \times 15 = 3375 \]

3. **Identifying Successful Attempts**:
- There is only **one successful attempt** to open the lock, which is the correct combination of letters.

4. **Calculating Unsuccessful Attempts**:
- The number of unsuccessful attempts can be calculated as:
\[ \text{Unsuccessful Attempts} = \text{Total Combinations} - \text{Successful Attempts} \]
- Substituting the values we have:
\[ \text{Unsuccessful Attempts} = 3375 - 1 = 3374 \]

5. **Conclusion**:
- Therefore, the number of ways \(N\) in which it is possible to make unsuccessful attempts to open the lock is:
\[ N = 3374 \]