11.1 Fundamental Counting Principle
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There are 4 shirts and 3 pairs of jeans, so using the fundamental counting principle, the number of possible outfit combinations is 4 * 3 = 12. The fundamental counting principle states that to calculate the number of possible outcomes of a series of events, you multiply the number of possible outcomes of each individual event. Examples are given of using this principle to calculate the number of possible 3-course meal combinations from various options, ways to customize a car order, and possible answers to a 10-item multiple choice quiz. The document also calculates the number of possible 10-digit telephone numbers in the US.
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This document provides information about recurrence relations and their applications in higher mathematics. It begins by introducing different types of sequences and exploring whether they can be described by a formula or recurrence relation. It then discusses linear recurrence relations and how they can model growth and decay scenarios. The document also covers divergence and convergence of sequences, and provides examples of applying recurrence relations to problems involving populations, waste disposal, medication in hospitals, and other scenarios.
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Probability is a branch of mathematics that studies patterns of chance. It is used to quantify the likelihood of events occurring in experiments or other situations involving uncertainty. The probability of an event is expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty. Key concepts in probability include theoretical and experimental probability, sample spaces, events, mutually exclusive and exhaustive events, and rules like addition rules for calculating combined probabilities. Probability is applied in many fields including statistics, gambling, science, and machine learning.
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Here are the solutions:
a) 6 x 6 = 36 (there are 2 tasks, rolling the die each time)
b) 6 x 6 x 6 = 216 (there are 3 tasks)
c) 6 x 6 x 6 x 6 = 1,296 (there are 4 tasks)
d) 6^k (by the product rule, there are k tasks, with 6 possible outcomes for each task)
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(7) Lesson 9.5
To find the sample space and probability of having cereal A with strawberries:
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Chapter 6
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11.1 Fundamental Counting Principle
- 1. 11.1 Fundamental Counting Principles (p. 559)
- 2. How many possible outfit combination can you form if you have 4 shirts and 3 pairs of jeans? 12
- 3. Fundamental Counting Principle The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur.
- 4. Example 1 A restaurant offers 5 appetizers, 20 main courses and 10 desserts. In how many ways can you order a 3-course meal? 5 x 20 x 10 = 1000
- 5. Example 2 In how many ways can a car be ordered if there are 5 possible colors, if it is automatic or standard, if it is powered by gas, electric or hybrid, and if it comes with or without GPS? 5 x 2 x 3 x 2 Answer: 60 ways
- 6. Example 3 You are taking a 10-item quiz with 5 possible choices. If you leave nothing blank, in how many ways can you answer the quiz? 9765625
- 7. Example 6 from the text Telephone numbers in the US begin with 3-digit area codes followed by 7-digit local telephone numbers. Area codes and local telephone numbers cannot begin with 0 or 1. How many different phone numbers are possible?
- 8. Answer 6 400 000 000 Note: We still run out of possible phone numbers because we don’t use all the area codes.
- 9. Assignments: Class work: Checkpoints 1-6 p. 560-563 Homework: p. 564, #s 1-22