# Ch 11: Probability Mechanics

### About This Chapter

## Probability Mechanics

If algebra doesn't normally excite you, you probably wouldn't expect to see exclamation points found in the expressions and equations you deal with. But did you know that the exclamation point is actually a part of proper math notation? In this series of lessons, (hopefully) the exclamation point that's used in factorials will get you excited!

So what is a factorial? In these lessons, you'll learn how a factorial signifies the multiplication of any integer by all the natural numbers that are smaller than it. For example, 4 factorial (notated as 4!) equals 4*3*2*1. Easy enough; however, factorials can yield some significantly large numbers. You'll learn the proper operation of factorials and get plenty of practice evaluating factorial problems. You'll learn how to shorten them, divide them and multiply them, as well as understand their real-life applications, which include how to determine the number of outcomes in a particular situation or how many arrangements of objects are possible.

Moving on in the world of probability mechanics, you'll learn about the binomial theorem. The binomial theorem gives us a method to expand binomials (expressions with two terms) that are being raised to an exponent. These are especially useful when you need to expand binomials that would be too time-consuming to expand using the F.O.I.L. method. You'll learn about how Pascal's Triangle can help you organize your information and avoid mistakes. You'll also learn how to evaluate abstract examples, handle an expression's coefficients, and learn, again, how this concept can be applied to real life.

So get excited (!) for your study of factorials and the binomial theorem. Thanks for watching!

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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!

### 5. Practice Problem Set for Probability Mechanics

If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.

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### Other Chapters

Other chapters within the Math 101: College Algebra course

- Foundations of Linear Equations
- Matrices and Absolute Value
- Inequalities
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Functions
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Sequences and Series
- Studying for Math 101