# Ch 19: Algebra II: Combinatorics

### About This Chapter

## Algebra II: Combinatorics - Chapter Summary and Learning Objectives

This chapter includes lessons focused on combinatorics, which is the study of countable (also known as finite) mathematical elements. You'll learn about the fundamental counting principle and the purpose of combinations when counting. Lessons also teach you about several probability rules, including the difference between independent and dependent events. Once you complete the chapter, you should have knowledge of the following topics:

- Fundamental counting principle
- Permutations and combinations
- Independent and dependent events
- Conditional probability

Video | Objective |
---|---|

Fundamental Counting Principle: Definition and Uses | Define and explain the use of the fundamental counting principle when dealing with combinatorics. |

How to Calculate a Permutation | Differentiate between permutations and combinations, discussing the purpose that combinations and permutations serve when counting. |

Math Combinations: Formula and Example Problems | Understand the factorial operation when counting down to factorials and show how to use math combinations in order to tell how many differing ways you may select an object from a larger group of items. |

Probability of Independent and Dependent Events | Differentiate between independent and dependent events, calculating each of these probabilities. |

Conditional Probability: Definition and Uses | Define conditional probability and its uses in the mathematical and practical world. |

### 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

Other chapters within the Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II