🔢 Module 2: Counting the Possibilities

Now that you speak probability's language, let's learn how to count its possibilities. This module arms you with mathematical tools to systematically count outcomes—the foundation for calculating probabilities accurately.

🧠 What You'll Learn

By the end of this module, you'll be able to:

  • 🧮 Apply the Fundamental Counting Principle to multi-step processes
  • 🔄 Distinguish between permutations and combinations
  • 📊 Calculate possible arrangements using factorial notation (!)
  • 👥 Solve real-world problems using counting techniques
  • 🚦 Determine when to use multiplication vs addition principles

📦 What's Inside

Topics in this module:

  • ✖️ 2.1 The Multiplication Principle (Fundamental Counting)
  • ❗ 2.2 Factorials and Their Probability Applications
  • 🔀 2.3 Permutations: Ordered Arrangements
  • 🥪 2.4 Combinations: Unordered Groups
  • 🌐 2.5 Real-World Applications

Decision Framework: When facing any counting problem, ask:

  1. Is order important? (Permutation)
  2. Are items repeatable?
  3. Are events dependent? This flowchart will become your best friend!

Professional Power Tools

These counting techniques are used daily in:

  • Data Science: Designing A/B tests
  • Cybersecurity: Calculating password combinations
  • Logistics: Optimizing delivery routes
  • Finance: Modeling portfolio outcomes

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