Permutations & Combinations 🔢

Before calculating probability, we often need to count the Total Cases (n) and Favorable Cases (m). P & C helps us count large numbers.

The Difference 🆚

• Permutation (P): Arrangement. Order matters.
• Combination (C): Selection. Order does NOT matter.

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1. Permutation (nPr) 📏

Used for arranging distinct objects.

• Example: Arranging 3 books on a shelf out of 5.
• 5P3 = 5! / (5-3)! = (5*4*3*) / 1 = 60 ways.

2. Combination (nCr) 🤲

Used for selecting teams, committees, cards.

• Example: Selecting 3 students from 5.
• 5C3 = 5! / (3! 2!) = 10 ways.
• Note: Picking A, B, C is same as C, B, A.

[!TIP] Factorial (!): n! = n * (n-1) * ... * 1 0! = 1

When to use in Probability? 🎲

Mostly we use Combinations for probability problems (Cards, Balls).

Example: Bag has 3 Red, 2 Blue balls. Draw 2 balls. Total ways to pick 2 from 5: 5C2. Ways to pick 1 Red and 1 Blue: 3C1 * 2C1.

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