Question

A store randomly assigns their employees work identificationnumbers to track productivity. Each number consists of 5 digits ranging from 1-9.If the digits cannot repeat, find the probability that a randomly generated numberis 25938.

Answer 1

In order to determine the probability of generating 25938 in exact order, let's determine first how many ways can we generate 5-digit numbers from 1 - 9.

So, for our first number, we have 9 numbers to choose from.

For our second number, we only have 8 numbers to choose from since digits cannot be repeated.

For our third number, we only have 7 numbers to choose from.

For our 4th number, we now have 6 numbers only available

Lastly, for our 5th number, only 5 numbers are available.

$9\times8\times7\times6\times5=15,120$

So, there are 15, 120 ways of generating 5-digit numbers out from 1-9 without digits being repeated. Out of these 15,120 ways, only one is 25938.

Hence, the probability that a randomly generated number is 25938 is:

$P(25938)=\frac{1}{15,120}$

or in decimal form,

$P(25938)=0.0000661$

or in percent form.

$P(25938)=.00661\%$