What is it?
The Permutation and Combination Calculator works out Permutations nPr, Combinations nCr and With repetition (n^r).
Who is it for?
Students preparing for school exams, JEE, CAT and other competitive tests, and anyone counting arrangements or selections.
How to use it
Enter n (total items) and r (items chosen). The answer appears as you type; there is no Calculate button. Tap Copy result to copy it, or Share on WhatsApp to send it.
Does order matter?
- Order matters → permutation: arranging 3 of 10 people as captain, vice-captain and treasurer: 10P3 = 720.
- Order doesn’t matter → combination: choosing a team of 3 from 10: 10C3 = 120.
- Repetition allowed: a 4-digit PIN from digits 0–9: 10⁴ = 10,000.
Exam tips
- nCr = nPr ÷ r!. Each group of 3 can be arranged 3! = 6 ways.
- nCr = nC(n−r): choosing 8 of 10 is the same as leaving out 2.
- Words with repeated letters (like BANANA) need division by the repeats: 6! ÷ (3! × 2!) = 60.
Very large n gives huge numbers shown in scientific notation; the Big Number Calculator gives every digit.
Worked example
Choosing 2 of 5 friends for a trip: 5C2 = 10; arranging 2 of 5 as driver and navigator: 5P2 = 20.
Errors and how to fix them
- “Use whole numbers with r ≤ n”: you can’t choose more items than you have.
- “Keep n at 1,000 or less”
Open the tool: Permutation and Combination Calculator
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Questions, or an error not listed here?
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