Introduction to Counting and Probability (Self Paced)

Fee: $70 - includes 14 video lessons and homework assignments ($5/lesson)

Note: Textbook is not included in the course fee. Please check AOPS, Amazon and other retailers to find the best price. Ask your friends if they have a copy from last year. Be sure to get both the textbook and the solutions manual. 

Textbook: https://artofproblemsolving.com/store/book/intro-counting

Textbook ISBN: 978-1-934124-10-9

Solutions ISBN: 978-1-934124-11-6

Introduction to Counting and Probability Lesson Plan:

• Class 1: Counting - Lists of Numbers, Arithmetic with Counting, and Permutations 

• Class 2: Counting Techniques - Casework, Complementary and Constructive Counting, and Restrictions 

• Class 3: Correcting for Overcounting - Permutations with Repeated Elements, Counting Pairs of Items, and Counting with Symmetries

• Class 4: Committees and Combinations - Committee forming, How to Compute Combinations and First Combinatorial Identity

• Class 5: More Combinations - Paths on Grids, More Committee-type Problems and Distinguishability

• Class 6: Counting Problems - More Advanced Counting Problems

• Class 7: Introduction to Probability - Basic Probability, Equally Likely Outcomes, and Counting Techniques in Probability 

• Class 8: Basic Probability Techniques - Probability and Addition, Complementary Probabilities, Probability and Multiplication and Probability with Dependent Events

• Class 9: Geometric Probability - Probability with Lengths and Areas

• Class 10: Expected Value - Definition of Expected Value and Expected Value Problems 

• Class 11: Pascal’s Triangle - Making Pascal’s Triangle and Combinatorial Identities 

• Class 12: The Hockey Stick Identity 

• Class 13: The Binomial Theorem - Application and Using Binomial Theorem in Identities

• Class 14: More Challenging Problems - Review of all Probability Techniques and advanced Problems