Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 10.2, Problem 59E
To determine
To calculate: The number of different outfits Don can wear if all items are compatible and Don has 2 pairs of shoes, 4pairs of pants, 6 shirts.
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Pidgeonhole Principle
1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined
as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest
integer greater than or equal to x. Try figuring out the answers to the following:
(a) [2.1]
(b) [2]
(c) [2.9]
(d) [2.1]
(e) [2]
(f) [2.9]
2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at
least one hole must have more than one item in it. We tried this with chairs and students: Assume you
have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on
it.
3. The general pidgeonhole principle states that, if you have N places and k items, then at least one
hole must have [] items or more in it. Try this out with
(a) n = 10 chairs and k = 15 students
(b) n = 10 chairs and k = 23 students
(c) n = 10 chairs and k = 20 students
4. There are 34 problems on these pages, and we…
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
Q2.2
1 Point
Determine if the set of vectors spans R³.
they span R³
they do not span R³
Save Answer
23
Q2.3
1 Point
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
1111
1110
Q2.4
1 Point
Determine if the set of vectors spans R4.
O they span R4
they do not span IR4
1000;
111O'
The everything combined problem
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to
directly connect a workstation to a server. For each server, only one direct connection to that server can be
active at any time.
1. How many cables would you need to connect each station to each server?
2. How many stations can be used at one time?
3. How many stations can not be used at any one time?
4. How many ways are there to pick 10 stations out of 15?
5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can
simultaneously access different servers via direct connections. What is the minimum number of direct
connections needed to achieve this goal?
Chapter 10 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...
Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Construct a product table showing all possible...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - 49. Find the number of paths from A to B in the...Ch. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Work each problem.
52. Shaking Hands in a Group A...Ch. 10.1 - Work each problem. Number of Games in a Chess...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Work each problem. Selecting Dinner Items Michael...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Work each problem. Building Numbers from Sets of...Ch. 10.1 - Work each problem. Lattice Points on a Line...Ch. 10.1 - Work each problem.
64. Lengths of Segments Joining...Ch. 10.1 - Work each problem. Patterns in Floor Tiling A...Ch. 10.1 - Work each problem, Counting Matchsticks in a Grid...Ch. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 9ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - Use a calculator to evaluate each expression. 10!Ch. 10.2 - Use a calculator to evaluate each expression.
18....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
23....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
26. ...Ch. 10.2 - Use a calculator to evaluate each expression.
27. ...Ch. 10.2 - Use a calculator to evaluate each expression.
28. ...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 34ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 36ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Matching Club Members with Tasks Recall the club...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 54ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - 62. Listing Phone Numbers Raj keeps the phone...Ch. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 67ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 69ECh. 10.2 - Work each problem. Palindromes How many of the...Ch. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.3 - Evaluate each expression. 9P3Ch. 10.3 - Evaluate each expression.
2.
Ch. 10.3 - Evaluate each expression.
3.
Ch. 10.3 - Evaluate each expression. 11P3Ch. 10.3 - Evaluate each expression.
5.
Ch. 10.3 - Evaluate each expression.
6.
Ch. 10.3 - Evaluate each expression. 10C8Ch. 10.3 - Evaluate each expression.
8.
Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Use a calculator to evaluate each expression. 22P9Ch. 10.3 - Use a calculator to evaluate each expression....Ch. 10.3 - Use a calculator to evaluate each expression.
19....Ch. 10.3 - Use a calculator to evaluate each expression.
20....Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Prob. 25ECh. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Prob. 36ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 4ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 8ECh. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Prob. 12ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 14ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 16ECh. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Prob. 20ECh. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - How many subsets (of any size) are there for a set...Ch. 10.4 - 28. For a given row in Pascal's triangle, let n be...Ch. 10.4 - 29. Which rows of Pascal's triangle have a single...Ch. 10.4 - 30. What is the least four-digit number in...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Tartaglia's Rectangle More than a century before...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.5 - How many proper subsets are there of each set?
1....Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Identifying Properties of Counting Numbers Flow...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Choosing Country Music Albums Jeanne's collection...Ch. 10.5 - Choosing Broadway Hits The ten longest Broadway...Ch. 10.5 - 23. Choosing Days of the Week How many different...Ch. 10.5 - Choosing School Assignments tor Completion Diona...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Seating Arrangements on an Airliner Refer to...Ch. 10.5 - 28. Identifying Properties of Counting Numbers...Ch. 10.5 - 29. Counting Radio Call Letters Radio stations in...Ch. 10.5 - 30. Selecting Faculty Committees A committee of...Ch. 10.5 - Selecting Search-and-Rescue Teams A Civil Air...Ch. 10.5 - Choosing Team Members Three students from a class...Ch. 10.5 - Prob. 33ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Prob. 35ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Prob. 39ECh. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Prob. 45ECh. 10.5 - Counting Card Hands Among the 2,598,960possible...Ch. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Triangles in a Figure Determine the...Ch. 10 - Tossing Coins Construct a tree diagram showing all...Ch. 10 - 7. Sums of Digits How many nonrepeating four-digit...Ch. 10 - 8. Arranging Children Yeo has invited her sister...Ch. 10 - Evaluate each expression. 6!Ch. 10 - Evaluate each expression. 8!6!Ch. 10 - Evaluate each expression.
11.
Ch. 10 - Evaluate each expression.
12.
Ch. 10 - Building Words from Sets of Letters How many...Ch. 10 - Building Words from Sets of Letters Using the...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball PlayersIf there are...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Prob. 23TCh. 10 - Prob. 24TCh. 10 - Prob. 25TCh. 10 - Prob. 26TCh. 10 - Prob. 27TCh. 10 - Prob. 28TCh. 10 - Prob. 29TCh. 10 - Prob. 30TCh. 10 - Prob. 31TCh. 10 - Prob. 32TCh. 10 - Prob. 33TCh. 10 - Prob. 34TCh. 10 - Prob. 35TCh. 10 - Prob. 36T
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