Permutations and Combinations

The product of first n natural

The product of first n natural numbers, denoted as n! = 1 × 2 × 3 × ... × n. By definition, 0! = 1. Used as the foundation for permutation and combina

Two basic rules

Two basic rules: Rule of Sum (Addition Principle) - when events are mutually exclusive, add the possibilities; Rule of Product (Multiplication Princip

Arrangements of objects where order matters

Arrangements of objects where order matters. Formula: ⁿPᵣ = n!/(n-r)! for arranging r objects from n distinct objects. With repetition: nʳ.

Arrangements in a circle where relative

Arrangements in a circle where relative positions matter. Formula: (n-1)! for n distinct objects. For necklaces/garlands where clockwise and anticlock

When some objects are identical

When some objects are identical, the formula becomes n!/(p₁! × p₂! × ... × pₖ!) where pᵢ represents the number of identical objects of each type.