🧭 Core Topics

Master the fundamental counting and probability concepts that form the foundation of AMC problems.

📚 Topic Overview

🔢 Basic Counting

• Counting Principles - Addition, multiplication, and complement rules
• Permutations & Combinations - Arrangements and selections
• Binomial & Multinomial - Advanced counting identities

🎯 Advanced Counting

• Inclusion-Exclusion - Overlapping set counting
• Pigeonhole Principle - Bounds and existence proofs
• Stars & Bars - Integer solution counting
• Symmetry & Invariance - Reducing cases through symmetry

🎲 Probability

• Probability Basics - Conditional probability and independence
• Expected Value - Linearity and indicators
• Distributions - Binomial, geometric, and hypergeometric

🔄 Advanced Topics

• Recurrences & Generating Functions - AMC 12 advanced techniques

🎯 Study Strategy

1. Start with Basic Counting - Master the fundamental principles
2. Practice Permutations & Combinations - These appear in most problems
3. Learn Advanced Counting - Essential for harder AMC problems
4. Master Probability - Critical for both AMC 10 and 12
5. Explore Advanced Topics - For AMC 12 and challenging problems

📊 Topic Dependencies

graph TD
    A[Counting Principles] --> B[Permutations & Combinations]
    B --> C[Binomial & Multinomial]
    A --> D[Inclusion-Exclusion]
    A --> E[Stars & Bars]
    B --> F[Probability Basics]
    F --> G[Expected Value]
    F --> H[Distributions]
    C --> I[Recurrences & GF]
    E --> I

🏆 Contest Tips

• AMC 10: Focus on basic counting, permutations/combinations, and simple probability
• AMC 12: Add advanced counting techniques, expected value, and distributions
• Time management: Use symmetry and complement principles to avoid casework
• Common traps: Watch for indistinguishable objects and replacement vs. no-replacement

Start with Counting Principles or jump to Permutations & Combinations

Next: Counting Principles | Back: Counting & Probability Mastery Guide