Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
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Chapter 13.2, Problem 60AYU

World Series In the World Series the American League team (A) and the National League team (N) play until one team wins four games. If the sequence of winners is designated by letters (for example, NAAAA means that the National League team won the first game and the American League won the next four), how many different sequences are possible?

Expert Solution & Answer
Check Mark
To determine

To find: How many different sequences are possible?

Answer to Problem 60AYU

Total of 70 different sequences is possible.

Explanation of Solution

Given:

In the World Series the American League team (A) and the National League team (N) play until one team wins four games. The sequence of winners is designated by letters (for example, NAAAA means that the National League team won the first game and the American League won the next four).

Formula used:

C( n, r ) =  n ! r!( n − r ) !

Calculation:

Consider the way American league wins.

To win the World Series they must win the last game.

Number of choices to win in 4 games - AAAA - C( 4, 1 ) − 4 .

Number of choices to win in 5 games-eg: AAANA - C( 4, 1 ) − 4 .

Number of choices to win in 6 games-eg: NAAANA - C( 5, 3 ) − 10 .

Number of choices to win in 7 games-eg: NNAAANA - C( 6, 3 ) − 20 .

If A wins the series then number of sequences is 35.

If N wins the series then number of sequences is 35.

Hence, total number of sequences is 35 + 35 = 70 .

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Chapter 13 Solutions

Precalculus Enhanced with Graphing Utilities

Ch. 13.1 - Prob. 1AYUCh. 13.1 - Prob. 2AYUCh. 13.1 - True or false The intersection of two sets is...Ch. 13.1 - Prob. 4AYUCh. 13.1 - Prob. 5AYUCh. 13.1 - If the number of elements in a set is a...Ch. 13.1 - Prob. 7AYUCh. 13.1 - True or False If a task consists of a sequence of...Ch. 13.1 - Prob. 9AYUCh. 13.1 - Prob. 10AYU
Ch. 13.1 - If n( A )=15 , n( B )=20 , and n( AB )=10 , find...Ch. 13.1 - If n( A )=30 , n( B )=40 , and n( AB )=45 , find...Ch. 13.1 - If n( AB )=50 , n( AB )=10 , and n( B )=20 , find...Ch. 13.1 - If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) ,...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - Shirts and Ties A man has 5 shirts and 3 ties. How...Ch. 13.1 - Blouses and Skirts A woman has 5 blouses and 8...Ch. 13.1 - Four-digit Numbers How many four-digit numbers can...Ch. 13.1 - Five-digit Numbers How many five-digit numbers can...Ch. 13.1 - Analyzing Survey Data In a consumer survey of 500...Ch. 13.1 - Analyzing Survey Data In a student survey, 200...Ch. 13.1 - Analyzing Survey Data In a survey of 100 investors...Ch. 13.1 - Prob. 30AYUCh. 13.1 - Demographics The following data represent the...Ch. 13.1 - Prob. 32AYUCh. 13.1 - Stock Portfolios As a financial planner, you are...Ch. 13.1 - Make up a problem different from any found in the...Ch. 13.2 - 0!= ; 1!= . (p. 642)Ch. 13.2 - True or False n!= ( n+1 )! n . (p. 642)Ch. 13.2 - A(n) __________ is an ordered arrangement of r...Ch. 13.2 - A(n) ___________ is an arrangement of r objects...Ch. 13.2 - P( n,r )= __________________.Ch. 13.2 - C( n,r )= _______________________.Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 4 objects 1,...Ch. 13.2 - List all the ordered arrangements of 6 objects 1,...Ch. 13.2 - List all the combinations of 5 objects a , b , c ,...Ch. 13.2 - List all the combinationss of 5 objects a , b , c...Ch. 13.2 - List all the combinations of 4 objects 1, 2, 3,...Ch. 13.2 - List all the combinationss of 6 objects 1, 2, 3,...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Lining People Up In how many ways can 4 people be...Ch. 13.2 - Stacking Boxes In how many ways can 5 different...Ch. 13.2 - Forming Codes How many different three-letter...Ch. 13.2 - Forming Codes How many different four-letter codes...Ch. 13.2 - Stocks on the NYSE Companies whose stocks are...Ch. 13.2 - Stocks on the NASDAQ Companies whose stocks are...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Possible Answers on a True/False Test How many...Ch. 13.2 - Possible Answers on a Multiple-choice Test How...Ch. 13.2 - Arranging Books Five different mathematics books...Ch. 13.2 - Forming License Plate Numbers How many different...Ch. 13.2 - Birthday Problem In how many ways can 2 people...Ch. 13.2 - Birthday Problem In how many ways can 5 people all...Ch. 13.2 - Forming a Committee A student dance committee is...Ch. 13.2 - Forming a Committee The student relations...Ch. 13.2 - Forming Words How many different 9-letter words...Ch. 13.2 - Forming Words How many different 11-letter words...Ch. 13.2 - Selecting Objects An urn contains 7 white balls...Ch. 13.2 - Selecting Objects An urn contains 15 red balls and...Ch. 13.2 - Senate Committees The U.S. Senate has 100 members....Ch. 13.2 - Football Teams A defensive football squad consists...Ch. 13.2 - Baseball In the American Baseball League, a...Ch. 13.2 - Baseball In the National Baseball League, the...Ch. 13.2 - Baseball Teams A baseball team has 15 members....Ch. 13.2 - World Series In the World Series the American...Ch. 13.2 - Basketball Teams A basketball team has 6 players...Ch. 13.2 - Basketball Teams On a basketball team of 12...Ch. 13.2 - Combination Locks A combination lock displays 50...Ch. 13.2 - Create a problem different from any found in the...Ch. 13.2 - Create a problem different from any found in the...Ch. 13.2 - Explain the difference between a permutation and a...Ch. 13.3 - When the same probability is assigned to each...Ch. 13.3 - The _____________of an event E is the set of all...Ch. 13.3 - True or False The probability of an event can...Ch. 13.3 - True or False In a probability model, the sum of...Ch. 13.3 - In a probability model, which of the following...Ch. 13.3 - In a probability model, which of the following...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - Prob. 25AYUCh. 13.3 - Prob. 26AYUCh. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - If P( A )=0.60 , P( AB )=0.85 , and P( AB )=0.05 ,...Ch. 13.3 - Prob. 50AYUCh. 13.3 - Prob. 51AYUCh. 13.3 - Prob. 52AYUCh. 13.3 - Prob. 53AYUCh. 13.3 - Doctorate Degrees According to the National...Ch. 13.3 - Prob. 55AYUCh. 13.3 - For Problems 57-60, a golf ball is selected at...Ch. 13.3 - Prob. 57AYUCh. 13.3 - Prob. 58AYUCh. 13.3 - Prob. 59AYUCh. 13.3 - Prob. 60AYUCh. 13.3 - On The Price Is Right, there is a game in which a...Ch. 13.3 - Prob. 62AYUCh. 13.3 - Prob. 63AYUCh. 13.3 - Prob. 64AYUCh. 13.3 - Prob. 65AYUCh. 13.3 - Prob. 66AYUCh. 13.3 - Prob. 67AYUCh. 13.3 - Checkout Lines Through observation, it has been...Ch. 13.3 - Prob. 69AYUCh. 13.3 - Prob. 70AYUCh. 13.3 - Prob. 71AYUCh. 13.3 - Birthday Problem What is the probability that at...Ch. 13.3 - Prob. 73AYUCh. 13 - Prob. 1RECh. 13 - If n( A )=8 , n( B )=12 , and n( AB )=3 , find n(...Ch. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - In Problems 10 and 11, compute the value of the...Ch. 13 - In Problems 10 and 11, compute the value of the...Ch. 13 - Stocking a Store A clothing store sells pure wool...Ch. 13 - Baseball On a given day, the American Baseball...Ch. 13 - Choosing Seats If 4 people enter a bus that has 9...Ch. 13 - Choosing a Team In how many ways can a squad of 4...Ch. 13 - Baseball In how many ways can 2 teams from 14...Ch. 13 - Telephone Numbers Using the digits 0, 1, 2,...,9,...Ch. 13 - Prob. 18RECh. 13 - Binary Codes Using the digits 0 and 1, how many...Ch. 13 - Arranging Flags How many different vertical...Ch. 13 - Forming Committees A group of 9 people is going to...Ch. 13 - Birthday Problem For this problem, assume that a...Ch. 13 - Unemployment According to the U.S. Bureau of Labor...Ch. 13 - Prob. 24RECh. 13 - Each of the numbers 1, 2,..., 100 is written on an...Ch. 13 - At the Milex tune-up and brake repair shop, the...Ch. 13 - Prob. 1CTCh. 13 - Prob. 2CTCh. 13 - Prob. 3CTCh. 13 - Prob. 4CTCh. 13 - Prob. 5CTCh. 13 - Prob. 6CTCh. 13 - Prob. 7CTCh. 13 - Prob. 8CTCh. 13 - Prob. 9CTCh. 13 - Prob. 10CTCh. 13 - Prob. 11CTCh. 13 - Prob. 12CTCh. 13 - Prob. 13CTCh. 13 - Prob. 14CTCh. 13 - Prob. 15CTCh. 13 - Prob. 16CTCh. 13 - Prob. 1CRCh. 13 - Prob. 2CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CR

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