The number lock of a suitcase has 4 wheels, each labelled with ten dig

1.	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» 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

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»

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

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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?

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