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

Exact permutations

Enter valid values to see the result.

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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.