Math 1320 Chapter 6: Sets and Counting 6.2 Cardinality.

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Presentation transcript:

Math 1320 Chapter 6: Sets and Counting 6.2 Cardinality

Definitions

Examples

Math 1320 Chapter 6: Sets and Counting 6.3 Decision Algorithms: The Addition and Multiplication Principles

Definition

Example A restaurant offers 3 main course salads, 4 pasta dishes, 3 beef meals, 2 chicken dinners, and 1 pork meal. This gives a total of = 13 main courses to choose from.

Definition

Example Hells Kitchen offers 3 appetizers, 5 main courses, and 2 desserts. You can create 3 X 5 X 2 = 30 different three course meals with that menu.

Examples 1.A surgical procedure requires four steps. The first can result in four possible outcomes, the second can result in three possible outcomes, and the remaining two can each result in two possible outcomes. What is the total number of outcomes possible? 2.A surgical procedure requires choosing among four alternative methodologies. The first can result in four possible outcomes, the second in three possible outcomes, and the remaining methodologies can each result in two possible outcomes. What is the total number of outcomes possible?

Definition A decision algorithm is a procedure in which we make a sequence of decisions. We can use decision algorithms to determine the number of possible outcomes by pretending we are designing such an item and listing the decisions or choices we should make at each stage of the process.

Example How many outcomes are possible? – Alternative 1: Step 1 has 1 outcome, step 2 has 2 outcomes. – Alternative 2: Step 1 has 2 outcomes, step 2 has 2 outcomes, and step 3 has 1 outcome.

Examples 1.Professor Easy’s final exam has 10 True-False questions followed by 2 multiple choice questions. In each of the multiple choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? 2.A test requires that you answer either part A or part B. Part A consists of 8 True-False questions and part B consists of five multiple choice questions with one correct answer in four. How many different completed answer sheets are possible?