🗺️ Chapter Roadmap
1 Factorials (n!)
A Factorial is the product of a positive integer and all the whole numbers below it, down to 1. It is represented by the symbol "!".
2 The Fundamental Counting Principle
Before learning complex formulas, you must know when to Multiply and when to Add. This is the foundation of all IQ probability and selection questions.
✖️ Multiplication Rule (AND)
If one event happens in m ways AND another happens in n ways, then both happen in m × n ways.
➕ Addition Rule (OR)
If you must choose between one event happening in m ways OR another in n ways, total ways = m + n.
3 & 4 Permutation vs. Combination
In exams like NTS, CSS MPT, or GAT, the biggest challenge is identifying which formula to use. The secret lies in one word: ORDER.
🏆 Permutation
Order Matters!
Use this for arrangements where the sequence is important (e.g., Passwords, sitting in a row, 1st/2nd/3rd prizes).
🥗 Combination
Order Doesn't Matter!
Use this for selections or groups where the order doesn't change the outcome (e.g., Committees, fruit salad, picking a team).
5 Key Differences Summary
| Feature | Permutation (P) | Combination (C) |
|---|---|---|
| Focus | Arranging | Selecting |
| Example | Phone numbers, PINs | Committees, Teams |
| Formula Size | Always Larger Value | Always Smaller Value |
| AB vs BA | AB and BA are Different | AB and BA are the Same |
📝 Deep Calculation Example:
Calculate 5C2 (Selecting 2 students from a group of 5).
5! / ( 2! × (5 − 2)! )
5! / ( 2! × 3! )
(5 × 4 × 3!) / ( 2 × 1 × 3! )