What is the likelihood of selecting a 4-digit number in the win-4 lottery, where one digit appears  exactly three times, given that each digit from 0 to 9 has an equal probability of being drawn in each of the four draws? Note that the number starts with 0 is a valid 4 digit-number such as 0001 is an option

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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What is the likelihood of selecting a 4-digit number in the win-4 lottery, where one digit appears  exactly three times, given that each digit from 0 to 9 has an equal probability of being drawn in each of the four draws? Note that the number starts with 0 is a valid 4 digit-number such as 0001 is an option

Expert Solution
Step 1: Probability obtained.

The sequence of 4-digit number may be

0 three times with one : 0001, 0010, 0100, 1000  = 4

Similarly o three times with other numbers. Total is 10*4 = 40

We have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 three times

 Number of  favourable arrangement is 10*40 = 400

Total number of arrangement is   10 to the power of 4 space equals 1000

Required probability = 400 over 1000=0.4

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