About This Chapter
Who's it for?
This unit of our High School Algebra II Homeschool course will benefit any student who is trying to learn about combinatorics. There is no faster or easier way to learn about combinatorics. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn how to work with the fundamental counting principle, calculate permutations, determine the probability of independent and dependent events or use conditional probability.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Combinatorics unit exam confirm understanding or identify any topics that require review.
Combinatorics Unit Objectives:
- Use the fundamental counting principle to determine how many different ways an event can occur.
- Explain why combinations and permutations are useful when counting.
- Discuss the difference between combinations and permutations.
- Differentiate between independent and dependent events.
- Calculate the probability of independent and dependent events.
- Use conditional probability to determine the likelihood of an event following the occurrence of some other event.
1. How to Use the Fundamental Counting Principle
There are many situations in which you will have to make several decisions simultaneously. The fundamental counting principle will help you determine how many different possible outcomes there are when you have to make multiple simultaneous decisions.
2. How to Calculate a Permutation
A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.
3. Math Combinations: Formula and Example Problems
Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.
4. Probability of Independent and Dependent Events
Sometimes probabilities need to be calculated when more than one event occurs. These types of compound events are called independent and dependent events. Through this lesson, we will look at some real-world examples of how to calculate these probabilities.
5. Conditional Probability: Definition & Uses
We know a coin can land on either heads or tails. But what would happen if one coin flip changed the next? In this lesson, we'll look at events that are dependent on each other, and we'll learn how to calculate the probability of two events occurring in a combined manner.
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Other chapters within the High School Algebra II: Homeschool Curriculum course
- Basic Arithmetic: Homeschool Curriculum
- Algebraic Equations: Homeschool Curriculum
- Real Numbers: Homeschool Curriculum
- Complex & Imaginary Numbers: Homeschool Curriculum
- Exponential Expressions: Homeschool Curriculum
- Properties of Functions: Homeschool Curriculum
- Linear Equations: Homeschool Curriculum
- Systems of Linear Equations: Homeschool Curriculum
- Inequalities: Homeschool Curriculum
- Matrices & Determinants: Homeschool Curriculum
- Absolute Value: Homeschool Curriculum
- Polynomials: Homeschool Curriculum
- Factoring: Homeschool Curriculum
- Factoring Quadratic Equations: Homeschool Curriculum
- Rational Expressions: Homeschool Curriculum
- Graphing & Functions: Homeschool Curriculum
- Roots & Radical Expressions: Homeschool Curriculum
- Quadratic Equations: Homeschool Curriculum
- Logarithmic Functions: Homeschool Curriculum
- Conic Sections: Homeschool Curriculum
- Sequences & Series: Homeschool Curriculum
- Sets in Algebra: Homeschool Curriculum
- Ratios & Percent: Homeschool Curriculum
- Statistics: Homeschool Curriculum
- Trigonometry: Homeschool Curriculum