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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?

10  The number lock of a suitcase has $\small 4$ wheels, each labelled with ten digits i.e., from $\small 0$ to $\small 9$. 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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Given, Each wheel can be labelled with 10 digits.

Number of ways of selecting 4 different digits out of the 10 digits = $^{10}\textrm{C}_{4}$

These 4 digits can arranged among themselves is $4!$ ways.

$\therefore$ Number of four digit numbers without repetitions =

$^{10}\textrm{C}_{4}\times4! = \frac{10!}{4!.6!}\times4! = 10\times9\times8\times7 = 5040$

Number of combination that can open the suitcase = 1

$\therefore$ Required probability of getting the right sequence to open the suitcase =  $\frac{1}{5040}$

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