Combinatorics Problem Sets – Based on A Path to Combinatorics for Undergraduates

This repository contains my organized solutions and study notes for Combinatorics, based primarily on the textbook
A Path to Combinatorics for Undergraduates by Titu Andreescu and Zuming Feng.

It serves as a personal study log and problem set archive as I work through core combinatorics concepts and example problems to deepen my problem-solving intuition and build a strong foundation for probability, statistics, and machine learning.

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Resource Used

All problems and theory are taken from:

Titu Andreescu & Zuming Feng, A Path to Combinatorics for Undergraduates
🔗 Link to book (if publicly available)

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Structure & Organization

Each folder corresponds to a major topic (loosely aligned with chapters in the book), and within it are subfiles for notes, problems, and solutions.

combinatorics-problem-sets/
├── 01_Addition_or_Multiplication/
│   ├── problem_01.ipynb
│   ├── problem_02.ipynb
│   ├── ...
├── 02_Combinations/
│   ├── ...
├── 03_Properties_of_Binomial_Coefficient/
│   ├── ...
├── ...
└── README.md

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How I'm Solving

Most problems are:

• Solved by hand on paper first
• Then written up in Markdown files for long-term reference
• Accompanied by distilled notes on key ideas and strategies
• Sometimes simulated or visualized (when helpful)

The goal is not speed, but true mastery — as part of my Project10X foundational training in probability and statistics.

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Learning Objectives

• Build deep problem-solving fluency in combinatorics
• Apply combinatorial techniques confidently in probability, inference, and AI
• Gain mastery of foundational tools like:
  • Product and sum rules
  • Permutations and combinations
  • Binomial identities
  • Inclusion-Exclusion
  • Pigeonhole principle
  • Integer partitions and distributions

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Progress Tracker (by topic)

• 01 Basic Counting Principles
• 02 Permutations and Factorials
• 03 Combinations and Binomial Identities
• 04 Pigeonhole Principle
• 05 Inclusion-Exclusion Principle
• 06 Distributions (Balls and Boxes)
• 07 Recursion and Combinatorial Proofs
• 08 Practice Sets and Mixed Review

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Tools Used

• Markdown + Git for organized version control
• LaTeX for clean math typesetting
• Optional: Python (Jupyter) for simulating and verifying complex counts

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📜 License

This repository is for educational and personal study use only.
All original problems and content are copyright of Andreescu and Feng.