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?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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 $10$ digits $=^{10} C_{4}$

Now, each combination of $4$ different digits can be arranged in $\lfloor 4$ ways.

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

There is only one number that can be open the suitcase.

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

Similar Questions

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

  • [AIEEE 2007]

Out of $13$ applicants for a job, there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.

All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is