Permutation and Combination Calculator
Calculate permutation and combination using your data.
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What this tool does
Calculate permutation and combination using your data. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
How to use the Permutation and Combination Calculator
- Enter or select n — items to choose from.
- Enter or select r — items chosen.
- Read the calculated result; change any measurement to compare alternatives.
Formula
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); with repetition: nPr = n^r, nCr = C(n+r−1, r)
- nn
- n — items to choose from
- rr
- r — items chosen
Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
Worked example
For permutation and combination calculator, the following measurements illustrate the exact method: n — items to choose from: 10; r — items chosen: 3.
Inputs
- n — items to choose from10
- r — items chosen3
Result
- Permutations nPr (order matters)720
- Combinations nCr (order does not matter)120
- Permutations with repetition (n^r)1,000
- Combinations with repetition C(n+r−1, r)220
- Factorial n!3,628,800
Results explained
- Permutations nPr (order matters)
- Permutations nPr (order matters) from the formula above. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
- Combinations nCr (order does not matter)
- Combinations nCr (order does not matter) from the formula above. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
- Permutations with repetition (n^r)
- Permutations with repetition (n^r) from the formula above. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
- Combinations with repetition C(n+r−1, r)
- Combinations with repetition C(n+r−1, r) from the formula above. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
- Factorial n!
- Factorial n! from the formula above. Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
Frequently asked questions
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); with repetition: nPr = n^r, nCr = C(n+r−1, r)
Permutations count arrangements (order matters, like podium finishes); combinations count selections (order does not matter, like committee members).
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.