Question

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

• A. $48$ divides N
• B. $N$ is the product of $3$ distinct prime numbers
• C. $N$ is the product of $4$ distinct prime numbers
• D. None of these

Answer 1

The correct option is B $N$ is the product of $3$ distinct prime numbers

The total number of possible permutations=$15\times 15\times 15=3375$

and out of all these permutations only one pattern will be the correct one.

Hence total number of unsuccessful attempts $=3375-1=3374=2\times 7\times 241$

Hence option B is correct.