Permutation AND Combination Calculator
Enter the size of a set (n) and the size of each sub-set (r) to get the number of permutations (order matters) and combinations (order does not matter), plus the variants that allow repetition — all with the factorial working.
TheCalculators — Permutation AND Combination Calculator
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Permutations nPr(6, 2)
30
Combinations nCr(6, 2) = 15
- Permutations (order matters) nPr
- 30
- Combinations (order ignored) nCr
- 15
- Permutations with repetition (nʳ)
- 36
- Combinations with repetition
- 21
- 6!
- 720
- 2!
- 2
- 4!
- 24
Formulas with substituted values
- 1Permutations formulanPr = n! / (n − r)! = 6! / (6 − 2)! = 6! / 4! = 30
- 2Combinations formulanCr = n! / (r! × (n − r)!) = 6! / (2! × 4!) = 15
- 3InterpretationFrom 6 items you can arrange 30 ordered selections of 2, but only 15 unordered groups.
Rule of thumb: if swapping two chosen items gives a different outcome (race podiums, PIN codes), use permutations; if it does not (lottery balls, committees), use combinations.
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Formula
nPr = n!/(n−r)! · nCr = n!/(r!·(n−r)!) · with repetition: nʳ and C(n+r−1, r)
Pro tips
- • nPr is always ≥ nCr because it counts each arrangement of every group separately.
- • Note nCr(n, r) = nCr(n, n − r) — choosing r to keep equals choosing n − r to discard.
- • Factorials explode fast: 70! already exceeds the number of atoms in the galaxy.
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