Permutation and Combination Calculator - Calculator See


Permutation and Combination Calculator

Calculate permutations nPr (where order matters) and combinations nCr (where order does not matter) with worked factorial steps.

Calculator Inputs

Total pool size.
Number chosen.

Calculated Results

Combinations nCr
252 Combinations
Permutations nPr (Order Matters) 30,240
Total Set Size (n) 10 Items
Subset Sample Size (r) 5 Items
Values calculate live as you adjust inputs.

About Permutation and Combination Calculator

Computes combinatorics values: Permutations (nPr) where selection sequence matters, and Combinations (nCr) where grouping order is irrelevant.

What is Permutation and Combination Calculator?

Computes combinatorics values: Permutations (nPr) where selection sequence matters, and Combinations (nCr) where grouping order is irrelevant.

How to Use This Calculator

  1. Enter total number of items n.
  2. Enter subset items chosen r (where r <= n).
  3. Compare permutations versus combinations.

The Mathematical Formula & Variables

nPr = n! / (n - r)!; nCr = n! / [r! * (n - r)!]

Step-by-Step Worked Example

Scenario: Selecting 5 items out of 10.

  1. 10! / (5! * 5!) = 3,628,800 / (120 * 120) = 252.
  2. nPr = 10! / 5! = 3,628,800 / 120 = 30,240.

Result: 252 combinations, 30,240 permutations

Frequently Asked Questions

What is the primary difference between combinations and permutations?

Order! A combination lock is technically a permutation lock because the order of numbers strictly matters.