Question

A number of lock on a suitcase has three wheels each labelled with ten digits $0$ to $9$. The opening of the lock is a particular sequence of three digits with no repeats. If a person tries to open the lock, then the number of unsuccessful attempts made by him is

• A. $719$
• B. $720$
• C. $1000$
• D. $999$

Answer 1

The correct option is A $719$

Number of ways to fill $1^{\text{st}}$ place $=10$
Number of ways to fill $2^{\text{nd}}$ place $=9$
Number of ways to fill $3^{\text{rd}}$ place $=8$
$\therefore$ Total number of ways to open the suitcase is $10\times 9\times 8=720$
Hence, the number of unsuccessful attempts made by him is $720-1=719$