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# Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

12 weeks

#### Diagnostics

ARE YOU READY? DO YOU NEED THIS?

SYLLABUS
12 weeks

## Schedule

### AoPS Holidays

There are no classes December 21 ‐ January 3, May 25 ‐ May 27, and July 4.

### Who Should Take?

This course is appropriate for students in grades 6-9 who have mastered basic algebra up through solving linear equations and manipulating multi-variable expressions. Students who have completed our Introduction to Algebra A course should have sufficient background. This course is roughly the same difficulty as our Introduction to Number Theory class. For those preparing for contests, this course should help with MATHCOUNTS and the AMC 8/10/12 tests.

### Lessons

 Lesson 1 Lists, Venn Diagrams, Addition, Multiplication Lesson 2 Casework, Constructions, and Restriction Lesson 3 Overcounting and Combinations Lesson 4 Combinations and Distinguishability Lesson 5 Challenging Problems Day Lesson 6 Introduction to Probability Lesson 7 Probability and Arithmetic Lesson 8 Geometric Probability, Think About It!, and Expected Value Lesson 9 Pascal's Triangle and Identities Lesson 10 Distributions and The Hockey Stick Identity Lesson 11 The Binomial Theorem Lesson 12 Challenging Problems Day 2

### Required Textbook Introduction to Counting & Probability By David Patrick A thorough introduction for students in grades 7-10 to counting and probability topics such as permutations, combinations, Pascal's triangle, geometric probability, basic combinatorial identities, the Binomial Theorem, and more. Related course: Introduction to Counting and Probability

I liked this class. The concepts seemed interesting and new and much better than what I would learn in school. I learned a lot about combinations and how they work. I really enjoyed this class.