Unit V DB Math

MAT 1301, Liberal Arts Math 1

Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to:

1. Apply mathematical principles used in real-world situations. 1.1 Tabulate elements in a set systematically. 1.2 Draw tree diagrams to represent counting situations graphically. 1.3 Apply the theory of permutations and combinations to solve counting problems.

5. Demonstrate counting techniques.

5.1 Apply the fundamental counting principle. 5.2 Calculate the number of permutations and combinations of n objects taken r at a time. 5.3 Use the factorial operation to evaluate expressions.

Required Unit Resources Chapter 12: Counting: Just How Many Are There?, Sections 12.1–12.3

Unit Lesson

Chapter 12: Counting: Just How Many Are There? Numbers and counting are some of the first mathematical principles that were introduced to you at a young age. We first learned how to count to 10; we then learned how to count to 100; and, eventually, we learned how to count by even and odd numbers. This unit expands our knowledge on basic counting strategies. For example, counting principles can describe the number of ways to perform certain tasks. These principles can be applied to many real-world situations. For instance, some sandwich shops offer an array of breads, meats, toppings, and sauces that can create an abundance of sandwich combinations. We can apply counting principles to identify the number of different sandwiches we could create using the number of choices given to us. Throughout this unit, you will learn how to count objects within a set systematically, how to draw tree diagrams, how to apply the fundamental counting principle, and how to apply the theory of permutations and combinations in order to solve counting problems. After you review the unit lesson, please complete the unit homework and assessment in MyLab Math.

Section 12.1: Introduction to Counting Methods In this section, we will learn how to apply different counting techniques in order to identify the number of ways to select objects from a given set. These methods are beneficial when the set of objects is large. Click the link to view the Section 12.1: Introduction to Counting Methods lesson.

Section 12.2: The Fundamental Counting Principle The fundamental counting principle utilizes the concept of a tree diagram to identify the number of ways a series of tasks can be completed by a using a simple formula.

UNIT V STUDY GUIDE

Counting

MAT 1301, Liberal Arts Math 2

UNIT x STUDY GUIDE

Title

Click the link to view the Section 12.2: The Fundamental Counting Principle lesson.

Section 12.3: Permutations and Combinations Have you ever tried several different combinations of letters and numbers in order to identify the correct password to a website? If so, then you have utilized the theory of permutations and combinations. Permutations and combinations are mathematical terms that are used when solving detailed counting problems. These principles help us identify the number of possible outcomes for a particular situation. Click the link to view the Section 12.3: Permutations and Combinations lesson.

Looking Forward After you review Sections 12.1, 12.2, and 12.3 of the unit lesson, begin your Unit V Homework assignment in MyLab Math. You will be instructed to watch several instructional videos before you complete your homework problems. It is recommended that you print the following reference sheet and note-taking guide to use while you watch the unit homework videos and complete the unit homework assignment.

• Unit V Reference Sheet

• Unit V Note-Taking Guide

Suggested Unit Resources In order to access the following resources, click the links below. The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please click the titles below to view the videos. Transcripts and closed captioning can be found when you click on the links below.

• Factorials video

• The Fundamental Counting Principle video

• Permutations and Combinations, Part I video

• Permutations and Combinations, Part II video

• Permutations and Combinations, Part III video

• Systematic Counting video

• Systematic Listing video

• Tree Diagrams video

MAT 1301, Liberal Arts Math 1

Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to:

1. Apply mathematical principles used in real-world situations. 1.1 Tabulate elements in a set systematically. 1.2 Draw tree diagrams to represent counting situations graphically. 1.3 Apply the theory of permutations and combinations to solve counting problems.

5. Demonstrate counting techniques.

5.1 Apply the fundamental counting principle. 5.2 Calculate the number of permutations and combinations of n objects taken r at a time. 5.3 Use the factorial operation to evaluate expressions.

Required Unit Resources Chapter 12: Counting: Just How Many Are There?, Sections 12.1–12.3

Unit Lesson

Chapter 12: Counting: Just How Many Are There? Numbers and counting are some of the first mathematical principles that were introduced to you at a young age. We first learned how to count to 10; we then learned how to count to 100; and, eventually, we learned how to count by even and odd numbers. This unit expands our knowledge on basic counting strategies. For example, counting principles can describe the number of ways to perform certain tasks. These principles can be applied to many real-world situations. For instance, some sandwich shops offer an array of breads, meats, toppings, and sauces that can create an abundance of sandwich combinations. We can apply counting principles to identify the number of different sandwiches we could create using the number of choices given to us. Throughout this unit, you will learn how to count objects within a set systematically, how to draw tree diagrams, how to apply the fundamental counting principle, and how to apply the theory of permutations and combinations in order to solve counting problems. After you review the unit lesson, please complete the unit homework and assessment in MyLab Math.

Section 12.1: Introduction to Counting Methods In this section, we will learn how to apply different counting techniques in order to identify the number of ways to select objects from a given set. These methods are beneficial when the set of objects is large. Click the link to view the Section 12.1: Introduction to Counting Methods lesson.

Section 12.2: The Fundamental Counting Principle The fundamental counting principle utilizes the concept of a tree diagram to identify the number of ways a series of tasks can be completed by a using a simple formula.

UNIT V STUDY GUIDE

Counting

MAT 1301, Liberal Arts Math 2

UNIT x STUDY GUIDE

Title

Click the link to view the Section 12.2: The Fundamental Counting Principle lesson.

Section 12.3: Permutations and Combinations Have you ever tried several different combinations of letters and numbers in order to identify the correct password to a website? If so, then you have utilized the theory of permutations and combinations. Permutations and combinations are mathematical terms that are used when solving detailed counting problems. These principles help us identify the number of possible outcomes for a particular situation. Click the link to view the Section 12.3: Permutations and Combinations lesson.

Looking Forward After you review Sections 12.1, 12.2, and 12.3 of the unit lesson, begin your Unit V Homework assignment in MyLab Math. You will be instructed to watch several instructional videos before you complete your homework problems. It is recommended that you print the following reference sheet and note-taking guide to use while you watch the unit homework videos and complete the unit homework assignment.

• Unit V Reference Sheet

• Unit V Note-Taking Guide

Suggested Unit Resources In order to access the following resources, click the links below. The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please click the titles below to view the videos. Transcripts and closed captioning can be found when you click on the links below.

• Factorials video

• The Fundamental Counting Principle video

• Permutations and Combinations, Part I video

• Permutations and Combinations, Part II video

• Permutations and Combinations, Part III video

• Systematic Counting video

• Systematic Listing video

• Tree Diagrams video