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 letter lock consisting of three rings marked with 15 different letters, we can follow these steps:

### Step 1: Understand the Total Combinations
Each of the three rings can be set to any of the 15 letters. Therefore, the total number of combinations for the lock can be calculated as follows:

\[ \text{Total combinations} = 15 \times 15 \times 15 = 15^3 \]

### Step 2: Calculate the Total Combinations
Now we calculate \(15^3\):

\[ 15^3 = 3375 \]

### Step 3: Determine the Successful Attempt
Since there is only one successful combination (the correct one), we subtract this from the total combinations to find the number of unsuccessful attempts:

\[ \text{Unsuccessful attempts} = \text{Total combinations} - \text{Successful attempt} \]

### Step 4: Calculate Unsuccessful Attempts
Substituting the values we have:

\[ \text{Unsuccessful attempts} = 3375 - 1 = 3374 \]

### Conclusion
Thus, the number of ways in which it is possible to make unsuccessful attempts to open the lock, denoted as \(N\), is:

\[ N = 3374 \]