Permutations & Combinations
Easy
10 mins read
Prerequisites
- Basic algebra multiplications
- Factorial values understanding
Introduction
Aptitude segment me permutations and combinations (P&C) counting calculations evaluate krne ke primary mechanisms hain. Inhe counting selections aur arrangements ke liye use kiya jata hai.
Real-Life Analogy
💡 Salad bowl vs Phone lock combination
Order of selection importance
| Concept Term | Real-life Analogy Mapping |
|---|---|
| Combination | Choosing vegetables for a Salad bowl. Order does not matter (tomato then onion = onion then tomato). |
| Permutation | Setting a Phone code lock password. Order matters (1-2-3 is different from 3-2-1). |
Detailed Concept Explanation
Permutations and Combinations standard expressions: - **Combination (nCr)**: Selecting r items from n choices (Order doesn't matter): `nCr = n! / (r! * (n - r)!)`. - **Permutation (nPr)**: Arranging r items from n choices (Order matters): `nPr = n! / (n - r)!`.
Visual Diagram
Pointer Variable (ptr)Address: 0x7ffd100
0x7ffd98b
Value is another Address
Points to
Normal Variable (x)Address: 0x7ffd98b
45
Actual integer value
Important Point
- nPr is always greater than or equal to nCr since arrangement counts are larger.
- nCr = nC(n-r).
Mnemonic / Memory Trick
P-A | C-S (Permutation Arrange | Combination Select)
Permutation = Arrangement | Combination = Selection
Mnemonic helper to recall selection vs arrangement classifications.
Avoid This Common Mistake
Students order constraints calculations checking circular seating arrangement formulas matching error.
GATE Exam Insights
Pipes and cisterns, permutations on word letters rearrangements and circular seating arrangements are high recurrence items.
Practice Mini Quiz
Revision Summary (One-Page Notes)
- •Combinations (nCr) select items; Permutations (nPr) arrange them.
- •Order distinguishes selection from arrangement.