CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Permutations with Repetition Calculator

Count ordered strings when every position may reuse an object type.

Counting & Combinatorics

Arrange objects with repetition

Order matters · repeats allowed
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Exact permutations

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Understand the subject

What is a permutation with repetition?

This counts ordered strings when each position may reuse any available symbol. Each new position starts with the full set of choices again.

Use it for codes, repeated draws with replacement, and ordered symbol strings.

The relationship

The counting rule

See the structure

Every position receives the full choice set

Worked example

Check the rule with a small case

Four digit strings allow 10⁴ = 10,000 outcomes, including leading zeroes.

Interpret with care

Choose the right counting model

If a symbol cannot repeat, use the ordinary permutation model.

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 number of available symbols n.
  2. Enter the number of ordered positions r.
  3. Read the exact number of strings.

Calculation method

Apply the product rule to every position

Each of r positions independently has n choices, so the count is n raised to r.

Worked example

Four-digit strings

Ten digits may be reused in each of four positions.

10⁴ = 10,000

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.