Answered: A four-digit security code is randomly…

A four-digit security code is randomly selected from the numbers 0,0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, 7,7, 8,8, and 9.9. What is the probability that the code does not have any repeated digits?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 9ECP: A random number generator selects two integers from 1 to 30. What is the probability that both...

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Question

A four-digit security code is randomly selected from the numbers 0,0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, 7,7, 8,8, and 9.9.

What is the probability that the code does not have any repeated digits?

Expert Solution

Step 1

Four digit security code is randomly selected from the numbers 0,1,...,9

So, total number of digits = 10

The number of ways 4 digits can be selected for 4 digit code = $10 \times 10 \times 10 \times 10 = 10^{4}$

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