Problem

8. Eli's workplace provided a randomly generated 4-digit code, in which the digits cannot be used more than once. Determine the probability that a code consists of 4 different odd numbers?

Solution

Step 1 :Eli's workplace provided a randomly generated 4-digit code, in which the digits cannot be used more than once. We are asked to determine the probability that a code consists of 4 different odd numbers.

Step 2 :The total number of 4-digit codes that can be generated from 0-9 without repeating any digit is \(10P4\) (Permutation of 10 items taken 4 at a time).

Step 3 :The total number of 4-digit codes that can be generated from the 5 odd numbers (1, 3, 5, 7, 9) without repeating any digit is \(5P4\) (Permutation of 5 items taken 4 at a time).

Step 4 :The probability that a code consists of 4 different odd numbers is the ratio of the number of favorable outcomes (\(5P4\)) to the total number of outcomes (\(10P4\)).

Step 5 :Calculating the total number of outcomes, we get 5040.

Step 6 :Calculating the number of favorable outcomes, we get 120.

Step 7 :Dividing the number of favorable outcomes by the total number of outcomes, we get a probability of 0.023809523809523808.

Step 8 :Final Answer: The probability that a code consists of 4 different odd numbers is \(\boxed{0.0238}\).

From Solvely APP
Source: https://solvelyapp.com/problems/12323/

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