Combinations vs Permutations: When Order Matters
Published Apr 13, 2026 · 6 min read
The key question: does order matter?
Permutation (Order Matters)
P(n,r) = n! / (nβr)!
Use when: password digits, race finishing order, seating arrangements. How many 3-digit codes from digits 1-9? P(9,3) = 504.
Combination (Order Doesn't Matter)
C(n,r) = n! / (r!(nβr)!)
Use when: lottery numbers, team selection, pizza toppings. How many ways to choose 3 toppings from 10? C(10,3) = 120.
Quick Decision Guide
- Choosing a committee of 5 from 20 people β Combination (who's on the committee, not their positions)
- Choosing president, VP, treasurer from 20 β Permutation (specific roles matter)
- Lottery: pick 6 numbers from 49 β Combination (the order you pick doesn't matter)
- Lock code: 4 digits β Permutation (1234 β 4321)
Try it: Use our Permutation & Combination Calculator to calculate P(n,r) and C(n,r) for any values.
π Sources: Khan Academy NIST