Permutation & Combination Formula
Permutation & Combination formulas and a topic-wise mock test for quantitative aptitude placement exams like TCS NQT, Infosys, and Wipro. Revise, then practice.
Key Permutation & Combination Formulas
Permutation Fundamentals - Arrangement Problems
Permutation deals with arranging objects in a specific order. Order matters — ABC is different from BAC.
- nPr = n! / (n-r)! — Arranging r objects from n
- nPn = n! — Arranging all n objects
- Circular Arrangement: (n-1)!
- Identical Objects: n! / (p! × q! × r!)
- Example: Arrange 3 from 5 → 5P3 = 60; Circle of 4 → (4-1)! = 6
Combination Fundamentals - Selection Problems
Combination deals with selecting objects without considering order. ABC = CBA.
- nCr = n! / (r! × (n-r)!)
- nC0 = 1, nCn = 1
- Symmetry: nCr = nC(n-r)
- Pascal's Identity: nCr + nC(r-1) = (n+1)Cr
- Example: Select 3 from 7 → 7C3 = 35
Advanced Permutation & Combination Problems
Practical examples for arrangements and selections.
- Example 1: Arrange 5 in a row → 5! = 120 ways
- Example 2: Select 3 from 7 → 7C3 = 35 ways
- Example 3: 4 around circular table → (4-1)! = 6 ways
- Example 4: Arrange MISSISSIPPI (11 letters, M=1,I=4,S=4,P=2) → 11!/(1!4!4!2!) = 34650
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