Summer schedule is now available! Enroll today to secure your spot!

Need Help?

Need help finding the right class? Have a question about how classes work?

Click here to Ask AoPS!

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 lessons

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
12 lessons ARE YOU READY? DO YOU NEED THIS? SYLLABUS  

Schedule

Sunday
Feb 11 - Apr 28
7:30 - 9:00
PM ET
Feb 11 - Apr 28
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
CLOSED
Sunday
Feb 11 - Apr 28
7:30 - 9:00
PM ET
Feb 11 - Apr 28
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
CLOSED
Wednesday
Mar 6 - May 22
7:30 - 9:00
PM ET
Mar 6 - May 22
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Friday
Mar 22 - Jun 7
7:30 - 9:00
PM ET
Mar 22 - Jun 7
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Saturday
Mar 23 - Jun 15
1:00 - 2:30
PM ET  
Mar 23 - Jun 15
1:00 - 2:30 PM Eastern
12:00 - 1:30 PM Central
11:00 - 12:30 PM Mountain
10:00 - 11:30 AM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Monday
Apr 8 - Jul 1
7:30 - 9:00
PM ET
Apr 8 - Jul 1
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Tuesday
Apr 23 - Jul 9
7:30 - 9:00
PM ET
Apr 23 - Jul 9
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Sunday
May 12 - Aug 4
7:30 - 9:00
PM ET
May 12 - Aug 4
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Thursday
May 16 - Aug 8
7:30 - 9:00
PM ET
May 16 - Aug 8
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Wednesday
May 29 - Aug 14
7:30 - 9:00
PM ET
May 29 - Aug 14
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Friday
Jun 7 - Aug 23
7:30 - 9:00
PM ET
Jun 7 - Aug 23
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Tuesday
Jun 11 - Aug 27
4:30 - 6:00
PM ET  
Jun 11 - Aug 27
4:30 - 6:00 PM Eastern
3:30 - 5:00 PM Central
2:30 - 4:00 PM Mountain
1:30 - 3:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Monday
Jun 17 - Sep 9
7:30 - 9:00
PM ET
Jun 17 - Sep 9
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL
Tue & Thurs
Jul 9 - Aug 15
7:30 - 9:00
PM ET
Jul 9 - Aug 15
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390
$439 w/books
$390
With Books $439
ENROLL
Sunday
Jul 28 - Oct 20
7:30 - 9:00
PM ET
Jul 28 - Oct 20
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$439 w/books
$390 (~$33/week)
With Books $439
ENROLL

AoPS Holidays

There are no classes May 25 ‐ 27, July 4, August 30 ‐ September 2, and November 25 ‐ December 1.

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.