# 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 - Mathematics

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 = 10xx9xx8=270

Of all the possible sequences, only one sequence is successful.
∴ Number of unsuccessful sequences = 720- 1=719

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 30 | Page 16