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

Answer: (D)

Number of options on $1^{\text{st}}$ ring $=4$
Number of options on $2^{\text{nd}}$ ring $=4$
Number of options on $3^{\text{ rd}}$ ring $=4$
Number of options on $4^{\text{ rd}}$ ring $=4$
Number of options on $5^{\text{ rd}}$ ring $=4$
$\therefore$ Total number of ways of all the options
$=4\times 4\times 4\times 4\times 4=1024$
$\therefore$ Number of all possible unsuccesful attempt to open the lock is
$=1024-1=1023$