# Ch 22: Combinatorics & Probability

### About This Chapter

## Combinatorics and Probability - Chapter Summary and Learning Objectives

This chapter's lessons invite you into the world of combinations and calculations for probabilities. Learn about the Fundamental Counting Principle and permutations, including the use of factorial operations when counting down. Plenty of practice problems are offered for experience in math combinations and the Binomial Theorem. When you're finished, you should have a solid understanding of the following:

- Conditional probability
- Fundamental Counting Principle
- Binomial Theorem
- Comparing probability of independent and dependent events

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

How to Use the Fundamental Counting Principle | Discover how and when to use this counting principle. |

How to Calculate a Permutation | Learn about the reasons for using permutations when counting. |

Math Combinations: Formula and Example Problems | Find out how many different ways items from groups may be chosen. |

Probability of Independent and Dependent Events | Compare independent and dependent events and practice discovering related probabilities. |

Conditional Probability: Definition & Uses | Examine how to calculate conditional probabilities. |

What is the Binomial Theorem? | Learn this theorem and when it may come in handy. |

Binomial Theorem Practice Problems | Experience using the theorem through practical exercises. |

### 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.

### 6. What is the Binomial Theorem?

While the F.O.I.L. method can be used to multiply any number of binomials together, doing more than three can quickly become a huge headache. Luckily, we've got the Binomial Theorem and Pascal's Triangle for that! Learn all about it in this lesson.

### 7. Binomial Theorem Practice Problems

The binomial theorem can be a really helpful shortcut, but it can also be really confusing. Brush up on your skills with this useful rule in these practice problems!

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### Other Chapters

Other chapters within the Algebra 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs