Introduction to Counting and Probability - Summer 2025
Based on AOPS "Introduction to Counting & Probability" textbook
7 week course includes 14 classes - 90 minute each
Covers all 15 chapters/topics in details
This class is open for in-person and online
Class recordings will be provided in case students miss any session
Our Counting and Probability course is designed to provide students with a strong foundation in fundamental concepts, techniques, and problem-solving strategies in counting and probability. The curriculum is based on the AOPS Introduction to Counting & Probability textbook and covers a comprehensive range of topics, including basic counting principles, permutations, combinations, binomial theorem, geometric probability, expected value, and more.
Throughout the course, students will have access to a range of resources, including live classes, practice problems, and homework assignments. Our teaching approach emphasizes active learning, problem-solving, and critical thinking. We believe that by providing a strong foundation in counting and probability, students will be well-prepared for advanced math courses in middle and high school.
Introduction to Counting and Probability (Summer 2025)
Teacher: Narender Gupta
Class Schedule: Tuesday and Thursday: 5:00 - 6:30 pm ET
Week 1: June 17, 19
Week 2: June 24, 26
Week 3: July 1, 3
Week 4: July 8, 10
Week 5: July 15, 17
Week 6: July 22, 24
Week 7: July 29, 31
Fee is calculated based on 14 scheduled classes and there is no charge for holidays.
Fees: Pick any option below:
Full prepay: $378 (avg to $18/hour)
Pay as you go: $40.50/class
Fee is calculated based on 14 scheduled classes and there is no charge for holidays.
Promotions:
Returning students will get a 10% discount on tuition fee
All students will get 25% discount on contest registrations when paid along with tuition fee
Textbook: https://artofproblemsolving.com/store/book/intro-counting
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
Email MathCoachingNG@gmail.com your name, student name and grade if you are unable to submit google form.