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. $N$ is product of three distinct prime numbers.
• B. $N$ is product of $4$ distinct prime numbers.
• C. $N$ is product of $2$ distinct prime numbers.
• D. None of these

Answer 1

The correct option is A

$N$ is product of three distinct prime numbers.

The explanation for the correct option:

Total number of unsuccessful attempts $=$ total number of successful attempts $-1$

$\begin{array}{rcl}N& =& (15x15x15)-1\\ & =& 3374\\ N& =& 2x7x241\end{array}$

Therefore, $N$ is the product of three distinct prime numbers.

Hence, option (A) is correct.