Permutation with Repetition Calculator
Verified Calculation Engine
The online Permutation with Repetition Calculator helps you calculate instantly and solve problems related to Permutations Combinations. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Calculates permutations with repetition allowed: n^r = number of ways to arrange r objects from n objects with repetition.
Permutations with repetition = n^r
Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r
When repetition is allowed, each position has n choices
Inputs
Results
Worked Examples
Example 1: Basic
How many 3-digit numbers can be formed using digits 0-9 with repetition?
- n: 10
- r: 3
- permutation: 1000
- formula: 10^3 = 1000
Example 2: Board Level
How many ways to arrange 4 letters from {A, B, C} with repetition?
- n: 3
- r: 3
- permutation: 81
- formula: 3^4 = 81
About this calculator
Overview
Permutation with Repetition Calculator evaluates Permutation with Repetition for the math / permutations-combinations library. Primary input cue: n (Total Objects) [required]: Total number of objects (can be repeated). Method anchor: Permutations with repetition = n^r Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r. When repetition is allowed, each position .
When to use
Appropriate when permutation with repetition is the target quantity and the form fields match your known data.
Inputs explained
- n (Total Objects) [required]: Total number of objects (can be repeated)
- r (Positions) [required]: Number of positions to fill
Formula / method
Permutations with repetition = n^r Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r. When repetition is allowed, each position has n choices (calculator id: permutation-with-repetition-calculator).
Worked example
Worked values: n = 10, r = 3 → permutation = 1000, formula = 10^3 = 1000
Interpreting results
Read the primary output as permutation with repetition under the method on this page.
Assumptions
- Units (when shown) must be consistent across inputs for permutation with repetition. [permutation-with-repetition-calculator]
- Empty required inputs are not silently replaced with zeros for permutation with repetition.
- Real-number arithmetic is used unless permutation with repetition explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to permutation with repetition.
- Permutation with Repetition Calculator cannot invent missing inputs; incomplete forms stop short of a forged permutation with repetition value.
- Complex/branch cuts and undefined points are not always interactively annotated for permutation with repetition.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Permutations with repetition = n^r Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r. When repetition is allowed, each position has n choices (calculator id: permutation-with-repetition-calculator).
Example Calculation
Worked values: n = 10, r = 3 → permutation = 1000, formula = 10^3 = 1000
Frequently Asked Questions
What is Permutation with Repetition Calculator?
- Permutation with Repetition Calculator evaluates Permutation with Repetition for the math / permutations-combinations library. Primary input cue: n (Total Objects) [required]: Total number of objects (can be repeated). Method anchor: Permutations with repetition = n^r Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r. When repetition is allowed, each position .
How does Permutation with Repetition Calculator work?
- Permutations with repetition = n^r Each position can be filled in n ways, so total = n × n × ... × n (r times) = n^r. When repetition is allowed, each position has n choices (calculator id: permutation-with-repetition-calculator).
Why use this Math Numbers calculator?
- Appropriate when permutation with repetition is the target quantity and the form fields match your known data.