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.

Answer 1

Total number of digits = 10
The digits are not repeated in a sequence of three digits.
$\therefore$ required number of sequences
= $10\times 9\times 8=720$
$\therefore$ Total number of unsuccessful attempts
= 720-1= 719