# Why It Matters: Probability and Counting Principles

According to the news, the lottery jackpot is climbing by the hour. Long lines of dreamers are forming wherever lottery tickets are sold. While you don’t usually buy lottery tickets, it is getting tempting. Just imagine what you could do with $100 million dollars. Perhaps you could retire early or never even go to work. Maybe visit a beautiful island. All you need to do is pick the correct numbers, and the jackpot is all yours. It sounds easy enough; just six simple numbers. But how likely are you to win? And could you increase the likelihood of winning by purchasing more lottery tickets? To answer these questions, you need to know about permutations and combinations. So learn about them as you complete this module, and then we’ll return to the lottery at the end. Then you’ll be able to decide whether you want to stand in line to purchase a ticket.### Learning Objectives

Counting Principles- Solve counting problems using the Addition Principle and the Multiplication Principle.
- Solve counting problems using permutations and combinations involving n distinct objects.
- Find the number of subsets of a given set.
- Solve counting problems using permutations involving n non-distinct objects.
- Apply the Binomial Theorem

Probability

- Construct probability models.
- Compute probabilities of equally likely outcomes.
- Compute probabilities of the union of two events.
- Use the complement rule to find probabilities.
- Compute probability using counting theory.

## Licenses & Attributions

### CC licensed content, Original

- Why It Matters: Probability and Counting Principles.
**Authored by:**Lumen Learning.**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Numbered balls for lottery.
**License:**CC0: No Rights Reserved. - Beach bay.
**License:**CC0: No Rights Reserved.