πŸ”’ Combination & Permutation Calculator

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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

nC(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:

  1. Enter Your Values
    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.
  2. Configure Options
    Select any additional options such as computation mode, currency, time period, or precision level. The calculator updates automatically as you change values.
  3. View the Results
    The calculated result is displayed instantly with clear formatting. You can Copy the result to your clipboard or adjust input values to see how different scenarios affect the outcome.

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.

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