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Permutation and Combination Calculator.

Calculate nPr and nCr.

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01

Set your values

Results update as you type.

nPr: 720

nPr

0.000000
nCr: 120

nCr

0.000000
Selected result: 720

Selected result

0.000000

Results update automatically as you type.

Use Cases

Probability and Statistics Problems

Solve probability questions that involve arranging or selecting items, such as lottery odds, card combinations, or seating arrangements.

Example: Calculate the number of ways to choose 3 winners from 10 participants (nCr).

Combinatorial Counting in Mathematics

Use for homework, exam prep, or quick verification of combinatorial formulas in algebra, discrete math, or computer science.

Example: Find the number of possible 4-digit PINs without repetition (nPr).

Frequently Asked Questions

What is the difference between permutation (nPr) and combination (nCr)?
Permutation (nPr) counts the number of ways to arrange r items out of n, where order matters. Combination (nCr) counts the number of ways to choose r items out of n, where order does not matter. For example, nPr = n!/(n-r)! and nCr = nPr/r!.
How do I use the permutation and combination calculator?
Enter the total number of items (n) and the number of items to choose or arrange (r) in the respective fields. The calculator will display both nPr and nCr results instantly. Ensure r ≤ n and both are non-negative integers.
Can I calculate permutations and combinations for large numbers?
Yes, the calculator can handle large numbers, but results may become extremely large. For very large n and r, the output might be displayed in scientific notation or cause overflow. It's best to use it for moderate values.

Tips & Common Mistakes

Tips

  • Ensure r is less than or equal to n; otherwise, the result is zero or undefined.
  • Use the calculator to verify manual calculations, especially when dealing with factorials.
  • Remember that nPr = nCr × r!; you can cross-check results using this relationship.
  • For quick mental checks, note that nC0 = nCn = 1 and nP0 = 1.

Common Mistakes to Avoid

  • Entering r greater than n, which yields an invalid result.
  • Confusing nPr and nCr: forgetting that order matters for permutations but not for combinations.
  • Using negative numbers or non-integers for n or r, which are not valid inputs.

Last updated: August 13, 2026