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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
⇒ 10C1 × 9C1 × 8C1
⇒ 10 × 9 × 8
⇒ 720
Of all the possible sequences, only one sequence is successful.
∴ Number of unsuccessful sequences = 720 − 1 = 719.
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