# Ch 21: ACT Math: Probability, Combinations & Factorial

### About This Chapter

## ACT Math: Probability, Combinations and Factorial - Chapter Summary

You'll review essential pre-algebra skills in this chapter. An understanding of the topics in these lessons helps to form a foundation for the higher-level math skills:

- Probability: independent and dependent events
- Overlapping and non-overlapping events (either/or probability)
- Probability of compound and complementary events
- Calculating combinations and permutations
- Factorial

Watch the fun and engaging video lessons, review factorial and math combinations with the practice exercises, and then complete the self-assessment quizzes.

### ACT Math Objectives

The math test is a 60-minute, 60-question exam that analyzes your logic skills in solving practical problems, showing whether you're ready for entry-level college coursework. You won't need to recall complicated formulas, but the test does assume that you'll have an understanding of basic formulas and key computations.

The pre-algebra portion of the test makes up 23% of the problems. You'll demonstrate your ability to complete many of the following functions:

- Basic operations with whole numbers, fractions and decimals
- Factors
- Ratio, percent and proportion
- Basic counting techniques and simple probability
- Data collection and interpretations
- Understanding simple statistics

Once you've worked your way through our video lessons, quizzes and practice exercises, you can target any areas that need more review for the test. You'll receive an overall ACT math score on all 60 questions, in addition to three sub-scores for pre-algebra/elementary algebra, intermediate algebra/coordinate geometry and plane geometry/trigonometry.

### 1. 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.

### 2. Probability of Independent Events: The 'At Least One' Rule

Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.

### 3. Either/Or Probability: Overlapping and Non-Overlapping Events

Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.

### 4. Joint, Marginal & Conditional Frequencies: Definitions, Differences & Examples

Joint, marginal, and conditional frequencies are all part of analyzing categorical data and two-way tables. This lesson will help you learn the definitions and differences between each concept.

### 5. Probability of Simple, Compound and Complementary Events

Simple, compound, and complementary events are different types of probabilities. Each of these probabilities are calculated in a slightly different fashion. In this lesson, we will look at some real world examples of these different forms of probability.

### 6. What is Random Sampling? - Definition, Conditions & Measures

Random sampling is used in many research scenarios. In this lesson, you will learn how to use random sampling and find out the benefits and risks of using random samples.

### 7. 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.

### 8. How to Calculate the Probability of Combinations

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

### 9. 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.

### 10. How to Calculate the Probability of Permutations

In this lesson, you will learn how to calculate the probability of a permutation by analyzing a real-world example in which the order of the events does matter. We'll also review what a factorial is. We will then go over some examples for practice.

### 11. Fundamental Counting Principle: Definition & Examples

In this lesson, you will learn about the fundamental counting principle, a method for determining how many ways choices can be made from groups. Several examples will be given.

### 12. Set Theory, Venn Diagrams & Exclusive Events

In this lesson, we're going to go over the concepts of sets and Venn diagrams, as well mutually exclusive and non-mutually exclusive events in terms of how they all tie in together.

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### Other Chapters

Other chapters within the ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Parts of an Essay
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Number & Quantity
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Functions
- ACT Math: Types of Functions
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Inequalities
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Complex Numbers
- ACT Math: Exponentials and Logarithms
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Plane Geometry
- ACT Math: Lines and Angles
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Science Reasoning: Evaluating Models
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Word Meanings and Choice
- ACT Reading: Analyzing Reading Passages
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills
- ACT Prep Flashcards