   Chapter 9.2, Problem 29ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Consider the numbers 1 through 99,999 in their ordinary decimal representations. How many contain exactly one of each of the digits 2,3,4, and 5?

To determine

To find how many numbersfrom 1 to 99,999 contain exactly one of the digits 2,3,4and 5.

Explanation

Given information:

Consider the numbers 1 through 99,999 in their ordinary decimal representations.

Concept used:

According to the question, numbers are considered in the decimal form representation from 1 through 99,999. Now, user have to find the numbers that contains exactly one of each of the digits 2,3,4and 5.

Calculation:

As the number consists one of each of the digits 2,3,4and 5, so the total numbers from 1 through 99,999, will be a 4 -digit numbers and 5 -digit numbers.

Case 1 :

All the 4 -digit numbers from 1 through 99,999 that consists one of each of the digits 2,3,4and 5 is given as:

4!=24

It is because these four numbers can be interchanged in 24 way to create a new different 4 -digit number.

All the 5 -digit numbers from 1 through 99,999 that consists one of each of the digits 2,3,4and 5 is given as:

The fifth digit must be 0,1,6,7,8or 9. There are two cases to consider:

The fifth digit is 0 or user have 0,2,3,4,5, which user want to put in some order

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