Question

1. identification a store randomly assigns their employees work identification numbers 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 number is 25938.

Explanation:

Step1: Calculate total permutations

We need to find the number of 5 - digit numbers with non - repeating digits from 1 - 9. The number of permutations of \(n\) objects taken \(r\) at a time is given by the formula \(P(n,r)=\frac{n!}{(n - r)!}\). Here, \(n = 9\) (digits from 1 - 9) and \(r=5\) (since we are forming 5 - digit numbers). So, \(P(9,5)=\frac{9!}{(9 - 5)!}=\frac{9!}{4!}=\frac{9\times8\times7\times6\times5\times4!}{4!}=9\times8\times7\times6\times5 = 15120\).

Step2: Determine favorable outcomes

There is only 1 favorable outcome, which is the number 25938.

Step3: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So, \(P=\frac{1}{15120}\).

Answer:

\(\frac{1}{15120}\)