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: 5:30 - 7 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: $336 ($24 for each 90 minute class - Avg to $16/hour)
Pay as you go: $36/class
Class material is included in the fee. Fee is calculated based on 14 scheduled classes and there is no charge for holidays.
Interested in Asynchronous participation?
Instead of attending live classes, you'll watch the sessions recording during the same week. You’ll receive the same homework and materials just like our regular students.
Fee for asynchronous students: $140 (Avg to $10 for each 90 minute class)
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
Email MathCoachingNG@gmail.com your name, student name and grade if you are unable to submit google form.