Permutation vs Combination — Difference (with Table)
Permutation vs Combination compared side by side — a 7-row comparison table and 4 key points. Class 11-12 Maths, free and no sign-up.
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TL;DR: Permutation vs Combination compared side by side — a 7-row comparison table and 4 key points. Class 11-12 Maths, free and no sign-up.
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The main difference between Permutation and Combination: Permutations count arrangements where order matters, while combinations count selections where order doesn't matter. These counting principles are crucial
Permutation vs Combination — Comparison Table
| Basis | Permutation | Combination |
|---|---|---|
| Definition | Arrangements where order matters | Selections where order doesn't matter |
| Order importance | Changing order creates different permutation | Changing order doesn't create new combination |
| Formula | P(n,r) = n!/(n-r)! | C(n,r) = n!/(r!(n-r)!) |
| Example | ABC, BCA, CAB are different | ABC and BCA are the same |
| Count | Always larger number | Always smaller number |
| Use cases | Password, seating arrangements, rankings | Lottery, committee selection, choosing teams |
| Real example | Arranging 3 books in a row | Choosing 3 books from shelf |
Key Points
- Permutations are for ordered arrangements; combinations are for unordered selections
- P(n,r) is always equal to or greater than C(n,r)
- P(n,r) = C(n,r) x r! because each combination can be arranged in r! ways
- Most real-world counting problems use combinations