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 =¹⁰C₄
Now, each combination of 4 different digits can be arranged in 4! Ways.
∴ Number of four digits with no repetitions = 4! ¹⁰C₄  = 5040
There is only one number that can open the suitcase.

Thus, the required probability is 1/5040