Think You Can Win the Lottery? An Introduction to Combinatorics

In this class we will explore the basics of calculating combinations and permutations and make connections to calculating the odds of winning the lottery, cracking codes, etc. 

We will: 
Discuss the purpose of counting formulas using some common scenarios;
Explore the differences between combinations and permutations;
Derive the formulas for calculating combinations and permutations.

Then we will apply these concepts to some common interesting problems such as: 
What is the likelihood that you can guess your friend's locker combination? 
What are the chances that a monkey with a typewriter could randomly write a given sentence? 
. . . and of course . . . 
What are your chances of winning the lottery? 
 

Week 1
Permutations: We will explore Permutations, derive the formulas, and discuss how to know when each of the permutation formulas should be used. We will then practice with a variety of problems. 

Week 2
Combinations: We will explore Combinations, derive the formulas, and discuss how to know when each of the combination formulas should be used. We will then practice with a variety of problems. 

Week 3
Putting it all together! In this session we will explore a variety of combination and permutation problems and see how this knowledge can help to answer the question of, "What are my chances of winning the lottery?" and other mathematical probabilities.