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Question

The number lock of a suitcase has 4 wheels each labelled with ten digits i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

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Solution

Number of wheels in number lock of suitcase =4.

Now, first wheel can have any one of the tens digits from 0 to 9.
Since, repetition is not allowed, so second wheel can have any of the remaining 8 digits.
Similarly, third wheel can have any of the remaining 7 digits.
And fourth wheel can have any of the remaining 6 digits
So, number of four digit lock code that can be formed without repetition of digits =10×9×8×7=5040
So, total four digit numbers formed =5040
But since, the lock can open with only one of the all four digit numbers.
Hence, required probability =15040

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