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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.
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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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