math
Permutation and Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for choosing r items from n.
Permutations (nPr)
20
Combinations (nCr)
10
How it works
- 1Enter the total number of items (n) and how many you choose (r).
- 2Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered selections.
- 3If r is greater than n, the result is shown as "—".
Use cases
- Count how many ways to arrange or seat people.
- Work out lottery or card-hand combinations.
- Solve probability and counting homework.
Frequently asked questions
What is the difference between a permutation and a combination?
Permutations count arrangements where order matters (nPr = n!/(n−r)!). Combinations count selections where order does not (nCr = n!/(r!(n−r)!)).
What does nPr mean?
The number of ordered ways to choose r items from n. For example, 5P2 = 20.
What does nCr mean?
The number of unordered ways to choose r items from n. For example, 5C2 = 10.
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