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 1

The number lock has 4 wheels, each labelled with ten digits i.e., from 0 to 9.
Number of ways of selecting 4 different digits out of the 10 digits =$C_4^{20}$
Now, each combination of 4 different digits can be arranged in 4! ways.
∴Number of four digits with no repetitions=$C_4^{10}×4!=\frac{10!}{46!}×4!=7×8×9×10=5040$
∴Number of four digits with no repetitions
Thus, the required probability is $\frac{1}{5040}$.