Ch 18: ACT Math: Probability, Combinations & Factorial

About This Chapter

Need to brush up on probabilities, combinations, or factorials before taking the ACT? This chapter features engaging video lessons to teach you these concepts that you may encounter on the ACT exam. Quiz yourself with lesson quizzes to make sure you are ready for these questions!

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.

10 Lessons in Chapter 18: ACT Math: Probability, Combinations & Factorial
Probability of Independent Events: The 'At Least One' Rule

1. 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.

Either/Or Probability: Overlapping and Non-Overlapping Events

2. 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.

Probability of Simple, Compound and Complementary Events

3. 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.

How to Calculate the Probability of Combinations

4. 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.

How to Calculate the Probability of Permutations

5. 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.

Probability of Independent and Dependent Events

6. 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.

What Is a Factorial?

7. What Is a Factorial?

Maybe it's because I'm a math teacher, but when I watched the Olympics I found myself thinking about how many different ways the swimmers could have finished the race. In this video, you'll learn the answer to this question, why it's important and how it lead to the invention of the mathematical operation called the factorial.

Factorial Practice Problems

8. Factorial Practice Problems

While the definition of factorial isn't complicated, it's easy to make them trickier by throwing a lot of them together and adding in some fractions. Test your skills here with some algebraic examples that make you use factorials without many numbers.

Math Combinations: Formula and Example Problems

9. 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.

How to Calculate a Permutation

10. 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.

Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support