   Chapter 9.3, Problem 20ES ### 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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# (a) How many integers from 1 through 100,000 contain the digit 6 exactly once? (b) How many integers from 1 through 100, 000 contain the digit 6 at least once? (c) If an integer is chosen at random from 1 through 100,000, what is the probability that it contains two or more occurrences of the digit that it contains two more occurrences of the digit .

To determine

(a)

To find:

Integers from 1 through 100,000 that contain the digit 6 exactly once.

Explanation

Given information:

Integers from 1 through 100,000

Calculation:

We are interested in the integers from 1 to 100,000 that contain the digit 6 exactly once. Since 100,000 does not contain the digit 6, we can consider the integers 1 to 99,999 which are the integers with 5 digits (or less).

Location of the six: 5 ways (as the number has at most 5 digits)

First digit that is not a six: 9 ways (as there are 10 digits, but this digit cannot be a 6)

Second digit that is not a six: 9 ways (as there are 10 digits, but this digit ...

To determine

(b)

To find:

Integers from 1 through 100,000 that contain the digit 6 at least once.

To determine

(c)

To find:

The probability that an integers contains two or more occurrences of the digit 6, if it is chosen at random from 1 through 100,000.

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