   Chapter 9.3, Problem 3ES ### 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 999 do not have any repeated digits? (b) How many integers from 1 through 999 have at least one repeated digit? (c) What is the probability that an integer chosen at random from 1 through 999 ha at least one repeated digit?

To determine

(a)

To find how many integers from 1 through 999 do not have any repeated digits.

Explanation

Given information:

Hexadecimal numbers are constructed using the digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.

Concept used:

The number of distinct integers from 1 to 9 digit is 9.

Calculation:

Objective is to rind the number of integers from 1 through 999 do not have any repeated digits.

The number of integers from 1 through 999 with no repeated digits is as follows:

Here, one-digit numbers from 1 to 9 :

The number of integers from 1 to 9 with no repeated digits is 9.

Two-digit numbers are from 10 to 99 :

In tens place, there are 1 to 9 digits.

In one’s place, there are 0 to 9 digits

To determine

(b)

To find how many integers from 1 through 999 have at least one repeated digits.

To determine

(c)

To find the probability that an integer chosen at random from 1 through 999 has at least one repeated digit.

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