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Statistics & Combinatorics • Lesson 27 ⏱ 6 min read 📅 Updated Nov 2026

Permutations vs Combinations (nPr vs nCr): The Easy Difference

Learn when order matters (Permutations) vs when order does not matter (Combinations), with formulas, real-world examples, and lock combination myths.

The Big Difference

Permutations (nPr): Order MATTERS (e.g. race podium, phone password).
Combinations (nCr): Order DOES NOT MATTER (e.g. fruit salad, lottery ticket).

1st 2nd Order MATTERS (nPr) 🍎 🍌 Order DOES NOT Matter (nCr)
Permutation (Race Podium) vs Combination (Fruit Salad Selection)

Comparison Table: nPr vs nCr

FeaturePermutations (nPr)Combinations (nCr)
Does order matter?YES! (AB ≠ BA)NO! (AB = BA)
Formula
nPr = n!(n − r)!
nCr = n!r!(n − r)!
Typical ExamplesPodium finishes, locker codes, seat arrangementsPizza toppings, team selection, poker hands
Calculation (5 choose 2)5 × 4 = 20(5 × 4) / 2 = 10
Try It Yourself

Practice with Our Interactive Combinations & Permutations Calculator

Check your calculations or explore full step-by-step solutions instantly.

Open Combinations & Permutations Calculator →
Solved Step-by-Step Examples:5 Choose 2 Combinations (5C2)5 P 2 Permutations (5P2)
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: In which scenario does ORDER MATTER?

Question 2: How many ways can you choose 1st and 2nd place from 5 race runners?

Question 3: What is 5C2 (5 Choose 2)?