**MISSION 408**

# Permutations and Combinations

In this mission, you will calculate the number of outcomes associated with various random experiments, and some powerful counting techniques that will allow us to answer questions such as:

- What is the probability of cracking a 4-digit PIN code using the code 8362?
- What is the probability of cracking a 6-digit PIN code using the code 348821?
- What is the probability of winning the big prize in a state lottery if we use the numbers (3, 20, 37, 44, 45, 49)?

You'll learn about concepts such as rule of product, permutations, combinations, and how they help solve probability problems or count the number of possible outcomes. For instance, there are 10,000 possible permutations for a 4-digit PIN code. In this course, you'll learn about how to calculate and use that information, and why it matters.

Along with learning about permutations, you'll learn about combinations. Combinations are similar to permutations, but with combinations, the order of the elements in an arrangement does not matter. Again, you'll learn how to calculate these and why they're useful for data scientists.

You'll also learn what a factorial is and what it means in mathematics along with how it relates to permutations and combinations.

#### Objectives

#### Mission Outline

1. The Importance of Counting

2. Extending the Rule of Product

3. A More Concrete Example

4. With Replacement of Without Replacement

5. Permutations

6. More About Perrmutations

7. Sometimes Order Doesn't Matter

8. Combination Notation

9. Next Steps

10. Takeaways