CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Permutation Calculator (nPr)

Count selections without repetition when order matters.

Counting & Combinatorics

Arrange objects when order matters

Permutation · nPr
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Exact permutations

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Understand the subject

What is a permutation?

A <strong>permutation</strong> is an ordered selection. The same objects placed in a different order create a new outcome.

Use it for rankings, podium places, PIN positions, and ordered assignments without repetition.

The relationship

The counting rule

See the structure

Positions make order matter

Worked example

Check the rule with a small case

Award gold, silver, and bronze among 10 people: P(10,3) = 10 × 9 × 8 = 720.

Interpret with care

Choose the right counting model

Do not divide by r factorial when roles or positions make order meaningful.

Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.

Quick guide

How to use this calculator

  1. Enter the total number of distinct objects n.
  2. Enter the number of ordered positions r.
  3. Read the exact number of ordered selections.

Calculation method

Fill each ordered position

There are n choices for the first position, n−1 for the second, and so on for r positions.

Worked example

Award three places among ten people

First, second, and third place are different roles, so order matters.

P(10,3) = 10!/7! = 720

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.