Permutation and Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for any n and r. Find factorials and understand arrangements vs selections. Free and instant.
Permutation and Combination Calculator
toolznova.com • Free Calculator
How to Use
Calculate permutations and combinations in 3 steps.
Enter n
Enter total number of items (n).
Enter r
Enter number of items to choose (r).
Get Results
Click Calculate for nPr, nCr, and factorials.
Why ToolzNova?
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Results in milliseconds.
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Precise formulas every time.
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Mobile, tablet, desktop.
Why Calculate Permutations and Combinations?
- Probability: Counting arrangements is fundamental to probability.
- Lottery: Calculate odds of lottery combinations (nCr).
- Games: Card hands, dice arrangements, game outcomes.
- Statistics: Binomial distribution uses combinations.
- Scheduling: Arrange teams, tasks, and appointments.
- Cryptography: Password combinations and key spaces.
Tips & Examples
- Permutation (order matters): selecting 3 from 10 — 10P3 = 720.
- Combination (order doesn't matter): choosing 3 from 10 — 10C3 = 120.
- nPr = nCr × r! — permutations always ≥ combinations.
- nCr = nC(n-r) — choosing r is same as leaving out n-r.
- 5! = 120. 10! = 3,628,800. Factorials grow very fast.
- Lottery 6 from 49: C(49,6) = 13,983,816 combinations.
Free Permutation Combination Calculator Online
ToolzNova's free permutation and combination calculator computes nPr (permutations) and nCr (combinations) for any n and r, along with the factorials n! and r!.
Permutations count arrangements where order matters. Combinations count selections where order doesn't matter. Both are fundamental to probability, statistics, and combinatorics.
Formulas
nPr = n!/(n-r)! — ordered arrangements. nCr = n!/(r!(n-r)!) — unordered selections. Relationship: nPr = nCr × r!