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Permutation and Combination Calculator

Calculate permutation and combination using explicit client-side inputs.

Permutation and Combination Calculator Inputs

Results computed instantly — your data never leaves your device.

Live Permutation and Combination Calculator Results

Real-Time

Permutations P(n,r)

720

Ordered selections without replacement.

100% Client-SidePrivate & Secure

How to Use the Permutation and Combination Calculator

  1. 1

    Enter the population size n.

  2. 2

    Enter the number of selected items r.

  3. 3

    Review the ordered-selection result.

  4. 4

    Confirm that r is not greater than n.

Formula & Mathematical Basis

P(n,r) = n! ÷ (n−r)!.

Variable Key

n

Total items available

r

Items selected in order

📝 This route reports permutations, where order matters; invalid r values return a guarded zero.

Step-by-Step Examples

1

Arrange three items from five

Scenario: Use n = 5 and r = 3.

  1. 1.Compute 5! = 120.
  2. 2.Compute (5−3)! = 2! = 2.
  3. 3.Divide 120 by 2.
  4. 4.Obtain 60 ordered arrangements.
✅ There are 60 permutations when selecting and ordering three items from five.

Practical Use Cases

  • Count ordered schedules or assignments.
  • Compare ordered and unordered selection problems.
  • Support introductory combinatorics exercises.

Common Pitfalls

  • Using combinations when order matters.
  • Entering r greater than n.
  • Forgetting that factorials grow very quickly.

Frequently Asked Questions

Does this calculate combinations too?

No. It calculates P(n,r), where order matters.

What happens when r is zero?

There is one empty ordered selection mathematically; the production factorial formula returns 1.

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