Question

A letter lock contains $5$ rings each marked with four different letters. The number of all possible unsuccessful attempts to open the lock is

• A. $625$
• B. $1024$
• C. $624$
• D. $1023$

Answer 1

The correct option is D $1023$

Number of options on 1st ring is $4$
Number of options on 2nd ring is $4$
Number of options on 3rd ring is $4$
Number of options on 4th ring is $4$
Number of options on 5th ring is $4$
$\therefore$ Total number of attempts possible
$=4\times 4\times 4\times 4\times 4=1024$

We can open the lock only in one of the total attempts
$\therefore$ Number of all possible unsuccessful attempts to open the lock is $=1024-1=1023$