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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
There are only 10 ways in which a number can be placed in the first place. It can be any number from 0, 1, 2, ….9.
The second, third and fourth places can be filled in 9 × 8 × 7 ways.
Thus, the number of ways to form a four-digit number (without repetition) is
= 10 × 9 × 8 × 7
= 5040
There is only one correct number to open the lock.
∴ The probability of finding the correct order to open the briefcase = `1/5040`.
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