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

Number of wheels in number lock of suitcase $=4$.

$⊸⊸⊸⊸$

Now, first wheel can have any one of the tens digits from $0$ to $9$.

Since, repetition is not allowed, so second wheel can have any of the remaining $8$ digits.

Similarly, third wheel can have any of the remaining $7$ digits.

And fourth wheel can have any of the remaining $6$ digits

So, number of four digit lock code that can be formed without repetition of digits $=10\times 9\times 8\times 7=5040$

So, total four digit numbers formed $=5040$

But since, the lock can open with only one of the all four digit numbers.

Hence, required probability $=\frac{1}{5040}$