Combination with Repetition Calculator
Verified Calculation Engine
The online Combination 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 combinations with repetition allowed: (n+r-1)Cr = number of ways to choose r objects from n types with repetition.
Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!]
Also called 'stars and bars' method
When repetition is allowed, use formula (n+r-1)Cr
Inputs
Results
Worked Examples
Example 1: Basic
How many ways to choose 3 fruits from 4 types (apple, banana, orange, mango) with repetition?
- n: 4
- r: 3
- combination: 20
- formula: (4+3-1)C3 = 6C3 = 20
Example 2: Board Level
How many ways to choose 5 items from 3 types with repetition?
- n: 3
- r: 3
- combination: 21
- formula: (3+5-1)C5 = 7C5 = 21
About this calculator
Overview
Combination with Repetition Calculator evaluates Combination with Repetition for the math / permutations-combinations library. Primary input cue: n (Types of Objects) [required]: Number of distinct types. Method anchor: Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!] Also called 'stars and bars' method. When repetition is allowed, use formula (n+r-1)Cr.
When to use
Reach for Combination with Repetition Calculator to compare scenarios by changing one input at a time for combination with repetition.
Inputs explained
- n (Types of Objects) [required]: Number of distinct types
- r (Objects to Choose) [required]: Number of objects to choose (can repeat)
Formula / method
Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!] Also called 'stars and bars' method. When repetition is allowed, use formula (n+r-1)Cr (calculator id: combination-with-repetition-calculator).
Worked example
Worked values: n = 4, r = 3 → combination = 20, formula = (4+3-1)C3 = 6C3 = 20
Interpreting results
If combination with repetition looks implausible, re-check units and which field is optional vs required.
Assumptions
- Empty required inputs are not silently replaced with zeros for combination with repetition. [combination-with-repetition-calculator]
- Combination with Repetition is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless combination with repetition explicitly needs integers.
Limitations
- If multiple conventions exist for combination with repetition, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to combination with repetition.
- Complex/branch cuts and undefined points are not always interactively annotated for combination 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
Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!] Also called 'stars and bars' method. When repetition is allowed, use formula (n+r-1)Cr (calculator id: combination-with-repetition-calculator).
Example Calculation
Worked values: n = 4, r = 3 → combination = 20, formula = (4+3-1)C3 = 6C3 = 20
Frequently Asked Questions
What is Combination with Repetition Calculator?
- Combination with Repetition Calculator evaluates Combination with Repetition for the math / permutations-combinations library. Primary input cue: n (Types of Objects) [required]: Number of distinct types. Method anchor: Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!] Also called 'stars and bars' method. When repetition is allowed, use formula (n+r-1)Cr.
How does Combination with Repetition Calculator work?
- Combinations with repetition = (n+r-1)Cr = (n+r-1)! / [r!(n-1)!] Also called 'stars and bars' method. When repetition is allowed, use formula (n+r-1)Cr (calculator id: combination-with-repetition-calculator).
Why use this Math Numbers calculator?
- Reach for Combination with Repetition Calculator to compare scenarios by changing one input at a time for combination with repetition.