Permutations and Combination

Three basic principles form the foundation

Three basic principles form the foundation: 1) Addition Principle: When choosing one option from multiple categories, add the number of ways (A OR B =

For any natural number n

For any natural number n, factorial is defined as n! = n × (n-1) × (n-2) × ... × 2 × 1, with special case 0! = 1. Key properties: n! = n × (n-1)!, and

Arrangements of objects where order matters

Arrangements of objects where order matters. Formula: nPr = n!/(n-r)! for selecting r objects from n distinct objects. When all n objects are arranged

Selections of objects where order doesn't

Selections of objects where order doesn't matter. Formula: nCr = n!/[r!(n-r)!] = nPr/r!. Key properties: nCr = nC(n-r), nC0 = 1, nCn = 1. Pascal's ide

Step 1

Step 1: Identify if order matters (permutation) or not (combination). Step 2: Check for restrictions or special conditions. Step 3: Apply appropriate