Permutations & Combinations

Compute nPr and nCr for choosing and arranging items

Work out how many ways you can choose or arrange items. Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered groups. The difference is whether order matters.

Permutations (nPr)

336

Order matters

Combinations (nCr)

56

Order doesn't matter

How to Use This Calculator

  1. Enter n, the total number of items.
  2. Enter r, how many you're choosing or arranging.
  3. Read both nPr (permutations) and nCr (combinations).

Why Use This Calculator?

  • Counting possible lottery or raffle outcomes.
  • Figuring out how many ways to arrange people in seats.
  • Working out committee or team combinations.

Real-World Examples

Choose 2 from 5

5C2 = 10 — there are ten ways to pick an unordered pair from five items.

Arrange 2 from 5

5P2 = 20 — if order matters, there are twenty ordered arrangements.

Order matters

If you're picking two people for a committee, order doesn't matter, so use combinations. If you're picking a president and a vice-president, order matters, so use permutations — and you get a bigger number.

Frequently Asked Questions

Why is nPr larger than nCr?

Because permutations count every ordering as different. Combinations treat different orderings of the same items as one, so there are fewer.

What if r is bigger than n?

You can't choose more items than you have, so the calculator shows an error — adjust r to be less than or equal to n.

Does it handle large numbers?

Yes, though results grow extremely fast — choosing from even modest groups can produce very large numbers.

Important Disclaimer

Calculations are exact for whole-number inputs where r does not exceed n.

Privacy

Your entries stay in your browser and aren't stored or sent.

Related Calculators

Statistics Calculator

Mean, median, mode, standard deviation and more

Scientific Calculator

Advanced scientific calculations with trig, log, and more

Percentage Calculator

Calculate percentages, increases, and decreases

Fraction Calculator

Add, subtract, multiply, and divide fractions

Exponent Calculator

Calculate powers and exponents