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CalcivoTools

Permutation Calculator : Calculate nPr (Order Matters), Repetitions & Circular Arrangements

The Calcivo Permutation Calculator determines the number of ordered arrangements of r items chosen from a set of n elements. It evaluates standard permutations (nPr), permutations with repetition (nʳ), and circular permutations ((n-1)!).

Interactive Calculator

100% Client-Side Engine
Total Distinct Permutations
210
Factorial Expansion Steps
1. n! = 7! = 5040
2. (n - r)! = (7 - 3)! = 4! = 24
3. nPr = 5040 ÷ 24 = 210

Step-by-Step Examples

Arranging 3 Books from a Shelf of 7

Order matters: P(7, 3).

Inputs: Total Items (n): 7, Items Chosen (r): 3
Result: 210 Arrangements

7! / (7 - 3)! = 7! / 4! = 7 × 6 × 5 = 210.

How to Use This Tool

  1. Select arrangement mode: Without Repetition (nPr), With Repetition (nʳ), or Circular.
  2. Enter the total number of items in the set (n).
  3. Enter the number of items to arrange (r).
  4. Click Calculate to see the permutation count and factorial expansion steps.

Frequently Asked Questions

In permutations, the order of selection matters (e.g. a password or race finish). In combinations, the order does not matter (e.g. choosing a committee or lottery numbers).

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