Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Concept explainers

Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Question
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Chapter 9.6, Problem 24E

(a)

To determine

To find: The number of four digit number formed.

(a)

Expert Solution
Check Mark

Answer to Problem 24E

The number of ways to choose the number is 9000 .

Explanation of Solution

Given:

The given information is that the leading number is not zero.

Calculation:

The choices for the leading digit is other than zero, thus the total number of choice is 9 and for the other digits there are no restriction. Therefore the total number of choice for each digit is 10 . The total number ways in which the number is made is,

  9×10×10×10×10=9000

(b)

To determine

To find: The number of four digit number formed.

(b)

Expert Solution
Check Mark

Answer to Problem 24E

The number of ways to choose the number is 4536 .

Explanation of Solution

Given:

The given information is that the leading number is not zero and no repetition is allowed.

Calculation:

The leading number is not zero, then the number of choice is 9 .

The second number must not be repetition of the first therefor the number of choices is 9 .

The third number must not be repetition of the first and second number therefore the number of choices is 8 .

The fourth number must not be repetition of the first second and third number therefore the number of choices is 7 .

Thus, the number choices in which the four digit number is made is,

  9×9×8×7=4536

(c)

To determine

To find: The number of four digit number formed.

(c)

Expert Solution
Check Mark

Answer to Problem 24E

The number of ways to choose the number is 4000 .

Explanation of Solution

Given:

The given information is that the leading number is not zero and the number must be less than 500.

Calculation:

The leading number is not zero, then the number must be less than 500 , then the choice for the first digit is 1,2,3,4 .

There are no restriction on rest of the digits then the choice for each of the remaining digit is,

Thus, the number choices in which the four digit number is made is,

  4×10×10×10=4000

(d)

To determine

To find: The number of four digit number formed.

(d)

Expert Solution
Check Mark

Answer to Problem 24E

The number of ways to choose the number is 4500 .

Explanation of Solution

Given:

The given information is that the leading number is not zero and the number is even.

Calculation:

The leading number is not zero, then the number of choice is 9 .

There are no restriction on the second and the thirdnumbertherefore the choices for each of the number is 10

The fourth number must be even therefore the number of choices is 5 .

Thus, the number choices in which the four digit number is made is,

  9×10×10×5=4500

Previous
Chapter 9.6, Problem 23E
Next
Chapter 9.6, Problem 25E

Chapter 9 Solutions

Precalculus with Limits

Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - 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Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - Prob. 45ECh. 9.5 - Prob. 46ECh. 9.5 - Prob. 47ECh. 9.5 - Prob. 48ECh. 9.5 - Prob. 49ECh. 9.5 - Prob. 50ECh. 9.5 - Prob. 51ECh. 9.5 - Prob. 52ECh. 9.5 - Prob. 53ECh. 9.5 - Prob. 54ECh. 9.5 - Prob. 55ECh. 9.5 - Prob. 56ECh. 9.5 - Prob. 57ECh. 9.5 - Prob. 58ECh. 9.5 - Prob. 59ECh. 9.5 - Prob. 60ECh. 9.5 - Prob. 61ECh. 9.5 - Prob. 62ECh. 9.5 - Prob. 63ECh. 9.5 - Prob. 64ECh. 9.5 - Prob. 65ECh. 9.5 - Prob. 66ECh. 9.5 - Prob. 67ECh. 9.5 - Prob. 68ECh. 9.5 - Prob. 69ECh. 9.5 - Prob. 70ECh. 9.5 - Prob. 71ECh. 9.5 - Prob. 72ECh. 9.5 - Prob. 73ECh. 9.5 - Prob. 74ECh. 9.5 - Prob. 75ECh. 9.5 - Prob. 76ECh. 9.5 - Prob. 77ECh. 9.5 - Prob. 78ECh. 9.5 - Prob. 79ECh. 9.5 - Prob. 80ECh. 9.5 - Prob. 81ECh. 9.5 - Prob. 82ECh. 9.5 - Prob. 83ECh. 9.5 - Prob. 84ECh. 9.5 - Prob. 85ECh. 9.5 - Prob. 86ECh. 9.5 - Prob. 87ECh. 9.5 - Prob. 88ECh. 9.5 - Prob. 89ECh. 9.5 - Prob. 90ECh. 9.5 - Prob. 91ECh. 9.5 - Prob. 92ECh. 9.5 - Prob. 93ECh. 9.5 - Prob. 94ECh. 9.5 - Prob. 95ECh. 9.5 - Prob. 96ECh. 9.5 - Prob. 97ECh. 9.5 - Prob. 98ECh. 9.5 - Prob. 99ECh. 9.5 - Prob. 100ECh. 9.5 - Prob. 101ECh. 9.5 - Prob. 102ECh. 9.5 - Prob. 103ECh. 9.6 - Prob. 1ECh. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - 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Prob. 28ECh. 9.7 - Prob. 29ECh. 9.7 - Prob. 30ECh. 9.7 - Prob. 31ECh. 9.7 - Prob. 32ECh. 9.7 - Prob. 33ECh. 9.7 - Prob. 34ECh. 9.7 - Prob. 35ECh. 9.7 - Prob. 36ECh. 9.7 - Prob. 37ECh. 9.7 - Prob. 38ECh. 9.7 - Prob. 39ECh. 9.7 - Prob. 40ECh. 9.7 - Prob. 41ECh. 9.7 - Prob. 42ECh. 9.7 - Prob. 43ECh. 9.7 - Prob. 44ECh. 9.7 - Prob. 45ECh. 9.7 - Prob. 46ECh. 9.7 - Prob. 47ECh. 9.7 - Prob. 48ECh. 9.7 - Prob. 49ECh. 9.7 - Prob. 50ECh. 9.7 - Prob. 51ECh. 9.7 - Prob. 52ECh. 9.7 - Prob. 53ECh. 9.7 - Prob. 54ECh. 9.7 - Prob. 55ECh. 9.7 - Prob. 56ECh. 9.7 - Prob. 57ECh. 9.7 - Prob. 58ECh. 9.7 - Prob. 59ECh. 9.7 - Prob. 60ECh. 9.7 - Prob. 61ECh. 9.7 - Prob. 62ECh. 9.7 - Prob. 63ECh. 9.7 - Prob. 64ECh. 9.7 - Prob. 65ECh. 9.7 - Prob. 66ECh. 9.7 - Prob. 67ECh. 9.7 - Prob. 68ECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - Prob. 75RECh. 9 - Prob. 76RECh. 9 - Prob. 77RECh. 9 - Prob. 78RECh. 9 - Prob. 79RECh. 9 - Prob. 80RECh. 9 - Prob. 81RECh. 9 - Prob. 82RECh. 9 - Prob. 83RECh. 9 - Prob. 84RECh. 9 - Prob. 85RECh. 9 - Prob. 86RECh. 9 - Prob. 87RECh. 9 - Prob. 88RECh. 9 - Prob. 89RECh. 9 - Prob. 90RECh. 9 - Prob. 91RECh. 9 - Prob. 92RECh. 9 - Prob. 93RECh. 9 - Prob. 94RECh. 9 - Prob. 95RECh. 9 - Prob. 96RECh. 9 - Prob. 97RECh. 9 - Prob. 98RECh. 9 - Prob. 99RECh. 9 - Prob. 100RECh. 9 - Prob. 101RECh. 9 - Prob. 102RECh. 9 - Prob. 103RECh. 9 - Prob. 104RECh. 9 - Prob. 105RECh. 9 - Prob. 106RECh. 9 - Prob. 107RECh. 9 - Prob. 108RECh. 9 - Prob. 1CTCh. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Prob. 13CTCh. 9 - Prob. 14CTCh. 9 - Prob. 15CTCh. 9 - Prob. 16CTCh. 9 - Prob. 17CTCh. 9 - Prob. 18CTCh. 9 - Prob. 19CTCh. 9 - Prob. 1CLTCh. 9 - Prob. 2CLTCh. 9 - Prob. 3CLTCh. 9 - Prob. 4CLTCh. 9 - Prob. 5CLTCh. 9 - Prob. 6CLTCh. 9 - Prob. 7CLTCh. 9 - Prob. 8CLTCh. 9 - Prob. 9CLTCh. 9 - Prob. 10CLTCh. 9 - Prob. 11CLTCh. 9 - Prob. 12CLTCh. 9 - Prob. 13CLTCh. 9 - Prob. 14CLTCh. 9 - Prob. 15CLTCh. 9 - Prob. 16CLTCh. 9 - Prob. 17CLTCh. 9 - Prob. 18CLTCh. 9 - Prob. 19CLTCh. 9 - Prob. 20CLTCh. 9 - Prob. 21CLTCh. 9 - Prob. 22CLTCh. 9 - Prob. 23CLTCh. 9 - Prob. 24CLTCh. 9 - Prob. 25CLTCh. 9 - Prob. 26CLTCh. 9 - Prob. 27CLTCh. 9 - Prob. 28CLTCh. 9 - Prob. 29CLTCh. 9 - Prob. 30CLTCh. 9 - Prob. 31CLTCh. 9 - Prob. 32CLTCh. 9 - Prob. 33CLTCh. 9 - Prob. 34CLTCh. 9 - Prob. 35CLTCh. 9 - Prob. 36CLTCh. 9 - Prob. 37CLTCh. 9 - Prob. 38CLTCh. 9 - Prob. 39CLTCh. 9 - Prob. 1PSCh. 9 - Prob. 2PSCh. 9 - Prob. 3PSCh. 9 - Prob. 4PSCh. 9 - Prob. 5PSCh. 9 - Prob. 6PSCh. 9 - Prob. 7PSCh. 9 - Prob. 8PSCh. 9 - Prob. 9PSCh. 9 - Prob. 10PSCh. 9 - Prob. 11PSCh. 9 - Prob. 12PSCh. 9 - Prob. 13PSCh. 9 - Prob. 14PSCh. 9 - Prob. 15PSCh. 9 - Prob. 16PS
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