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?
Answer:
Given
Number of wheels in lock = 4
Digits are 0 to 9
Number of ways selecting 4 digits out of 10 digits = 10C4
Total number of combination of 4 different digits = 4!
Total number of four digits with no repetition = 4!* 10C4
= 10!/(4! *6!) * 4!
= 10!/6!
= (10*9*8*7*6!)/6!
= 10*9*8*7
= 5040
Suitcase can be open if any one sequence matches with four digits of the wheel.
So probability = 1/5040
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