The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e.,

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?

Solution:

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 $={ }^{10} \mathrm{C}_{4}$

$\therefore$ Number of four digits with no repetitions $={ }^{10} \mathrm{C}_{4} \times\left\lfloor 4=\frac{\lfloor 10}{|4| 6} \times\lfloor 4=7 \times 8 \times 9 \times 10=5040\right.$

There is only one number that can open the suitcase.

Thus, the required probability is $\frac{1}{5040}$.

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