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
$=1024-1=1023$