Question:
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Solution:
The digits in the sequence do not repeat.
Number of ways of selecting the first digit = 10
Number of ways of selecting the second digit = 9
Number of ways of selecting the third digit = 8
Total number of possible sequences $=10 \times 9 \times 8=720$
Of all the possible sequences, only one sequence is successful.
$\therefore$ Number of unsuccessful sequences $=720-1=719$