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 $\frac{1}{5040}$.