🔢 Permutation and Combination - Formula Sheet

🎯 Fundamental Principles

Addition Rule

Total ways = Ways₁ + Ways₂ + Ways₃
(When choices are mutually exclusive)

Multiplication Rule

Total ways = Ways₁ × Ways₂ × Ways₃
(When choices are independent)

📊 Permutation (Arrangement)

nPr Formula

nPr = n! / (n-r)!

Where:

• n = total items
• r = items to arrange
• n! = n × (n-1) × … × 1

Special Cases

n! = n × (n-1)!
0! = 1
1! = 1
n! / n! = 1

Circular Permutation

Number of ways = (n-1)!
When n distinct objects arranged in circle

🔢 Combination (Selection)

nCr Formula

nCr = n! / [r! × (n-r)!]

Properties

nCr = nC(n-r)
nC0 = nCn = 1
nC1 = nC(n-1) = n

Sum of Combinations

nC0 + nC1 + nC2 + ... + nCn = 2ⁿ

⚡ Applications

Word Formation

With repetition: n^r
Without repetition: nPr

Committee Formation

From m men and n women:
Select r people with specific conditions using combinations

Seating Arrangement

Linear: n!
Circular: (n-1)!
With restrictions: Adjust accordingly

📝 Problem Types

Arrangement Problems

1. Total arrangements: Use permutation
2. With restrictions: Count valid arrangements
3. With repetition: Use multiplication principle

Selection Problems

1. Team/committee: Use combination
2. With conditions: Apply restrictions
3. Multiple groups: Use combination for each

🔍 Quick Tips

1. Arrangement = Permutation
2. Selection = Combination
3. Always consider restrictions first
4. Use complement method for complex cases

Master P&C - Practice different problem types! 🔢