Mathematical Ideas (13th Edition) - Standalone book
Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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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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Chapter 10.5, Problem 27E

Seating Arrangements on an Airliner Refer to Example 3. If one of the group decided at the last minute not to fly, then how many ways could the remaining three arrange themselves among the ten available seats so that at least one of them would sit on the aisle?

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Chapter 10 Solutions

Mathematical Ideas (13th Edition) - Standalone book

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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