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 possible numbers

We need to find the number of permutations of 9 digits taken 5 at a time. The formula for permutations is $P(n, r)=\frac{n!}{(n - r)!}$, where $n = 9$ and $r=5$.
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

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}=\frac{1}{15120}$.

Answer:

$\frac{1}{15120}$