Question:
A number lock on a suitcase has three wheels each labeled 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 number of sequences possible $=10 \times 9 \times 8=720($ since no repeated digits is the given condition.)
There will be only one successful attempt so the number of unsuccessful attempts to open the lock $=720-1=719$.