The Combination Calculator is your ultimate tool to instantly calculate nCr values with precision and ease. Whether you’re solving probability problems, studying statistics, or exploring combinations and permutations, this calculator gives you accurate, step-by-step results in seconds. Designed for students, teachers, and data analysts, our online combination solver helps you understand the math behind every calculation making complex formulas simple and practical.
🔢 Combination Calculator
Use this nCr calculator to easily calculate the number of combinations given a set of objects (types) and the number to choose from the set.
Combination Calculator
Use this Combination Calculator to easily find the total number of possible combinations for any given set of items. Whether you’re solving a probability problem, planning statistical experiments, or analyzing data sets, this calculator provides quick and accurate results using the standard nCr formula.
What is a Combination?
A combination is a way of selecting items from a larger group, where the order does not matter. For example, choosing 2 fruits from a basket of 5 is a combination problem, since “apple and banana” is the same as “banana and apple.”
Combination vs. Permutation
In a permutation, the order of selection matters (ABC ≠ BCA), while in a combination, the order does not matter (ABC = BCA). Use a Permutation Calculator when sequence matters, and a Combination Calculator when it doesn’t.
Combination Formula
The mathematical formula to calculate combinations is given by:
Explanation of Terms
- n = total number of items
- r = number of items chosen
- ! = factorial (the product of all positive integers up to that number)
Example Calculation
Let’s say we want to calculate the number of ways to choose 2 items from a group of 5. Using the formula:
C(5, 2) = 5! / [2! × (5 − 2)!]
= 120 / (2 × 6) = 10 combinations
How to Use the Combination Calculator
- Enter the total number of items (n).
- Enter the number of items to choose (r).
- Click the Calculate button to get instant results.
- The calculator will display the number of possible combinations based on the given inputs.
Applications of Combinations
Combinations are widely used in various fields such as:
- Probability and Statistics – determining outcomes where order doesn’t matter.
- Data Science – feature selection and sampling analysis.
- Card Games and Lottery – calculating possible hands or winning combinations.
- AI and Machine Learning – generating feature subsets for modeling.
Difference Between Combination and Permutation
The main difference lies in whether order matters:
| Aspect | Combination | Permutation |
|---|---|---|
| Order | Does not matter | Matters |
| Formula | n! / [r! × (n − r)!] | n! / (n − r)! |
FAQs About Combination Calculator
What is the formula for combinations?
The formula for combinations is C(n, r) = n! / [r! × (n − r)!], where n is the total number of items and r is the number of items selected.
How do combinations differ from permutations?
In combinations, the order of items doesn’t matter, while in permutations, it does.
Can I calculate combinations for large numbers?
Yes, this calculator can handle large numbers instantly using factorial simplification methods, giving accurate results without manual calculations.
Where are combinations used in real life?
Combinations are used in probability, statistics, card games, data science, and machine learning for counting and sampling problems.
Is this Combination Calculator accurate?
Yes, this tool uses precise mathematical logic and is tested for both small and large datasets, ensuring highly accurate outputs.
About This Tool
Our Combination Calculator is designed to simplify complex nCr calculations in seconds. It’s ideal for students, statisticians, and data analysts who need to calculate combinations quickly and accurately. This tool uses modern algorithms to provide reliable results with an intuitive interface that’s easy to use on any device.