Module 1: Combinatorics & Counting

Combinatorics is the foundation of probability. Before we can calculate the likelihood of an event, we must be able to count the total number of possible outcomes. This module covers the essential counting principles, from basic permutations to advanced inclusion-exclusion logic.

Module Contents

  1. Permutations & Combinations
    • Learn the Fundamental Counting Principle.
    • Understand when order matters (Permutations) and when it doesn’t (Combinations).
    • Interactive Visualizer: Compare nPr vs nCr.
  2. Binomial Theorem
    • Master the expansion of (x+y)n.
    • Explore Pascal’s Triangle interactively.
    • See how this applies to Polynomial Kernels in Machine Learning.
  3. Inclusion-Exclusion Principle
    • Solve the problem of double counting in set unions.
    • Interactive Venn Diagram solver for 2 and 3 sets.
    • Real-world application: Calculating Monthly Active Users (MAU).
  4. Module Review
    • Flashcards: Test your knowledge.
    • Cheat Sheet: All formulas in one place.
    • Key Takeaways: Summary for quick revision.