Updated: 2026-07-11
Parameters
Results
C(10,3) = 120
Combinations C(n, r)
β
Permutations P(n, r)
β
n!
β
(n-r)!
β
Ratio C/P
β
Order of Magnitude
β
Click "Calculate" to see step-by-step solution
Reference: Common Combination Values
| n | C(n,1) | C(n,2) | C(n,3) | C(n,4) | C(n,5) |
|---|
How to Use the Combination & Permutation Calculator
Using the Combination & Permutation Calculator is straightforward:
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Input the required numbers and parameters into the calculator fields. Each field is clearly labeled β simply type your values or use the spinner controls to adjust them. -
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FAQ
What's the difference between combinations and permutations?
Permutations (P(n,r)) consider the order of elements β order matters. Combinations (C(n,r)) do not consider order β order doesn't matter. E.g., from ABC choosing 2: permutations give AB,BA,AC,CA,BC,CB (6); combinations give AB,AC,BC (3).
What are the formulas?
Combinations: C(n,r) = n! / (r! Γ (n-r)!)
Permutations: P(n,r) = n! / (n-r)!
What is C(n,0)?
C(n,0) = 1. There's exactly one way to choose nothing from n items. Similarly, C(n,n) = 1.
Real-world applications?
Combinations and permutations are used in probability and statistics (lottery odds, poker hands), cryptography (possible password combinations), computer science (algorithm analysis), and many other fields.