# Combination Calculator

Calculate combinations (C(n,r)) with support for different types: with/without repetition, binomial coefficients, and detailed combinatorial analysis.

> Canonical page: https://elysiatools.com/en/tools/combination-calculator

- **Category:** Math & Numbers

- **Keywords:** combination, binomial, choose, combinatorics, mathematics, C(n,r), n choose k

## Overview

The Combination Calculator is a precise mathematical tool designed to compute the number of ways to select items from a larger set, supporting both standard combinations and combinations with repetition.

## Inputs

- **Total Items (n)** (number): Total number of distinct items
- **Items to Choose (r)** (number): Number of items to select
- **Combination Type** (select)
- **Show mathematical formula** (checkbox)
- **Show calculation steps** (checkbox)
- **Show Pascal triangle position** (checkbox)

## When to use

- When determining the number of possible outcomes in probability and statistics problems.
- When calculating binomial coefficients for algebraic expansions or discrete mathematics.
- When solving real-world selection scenarios where the order of items does not matter.

## How it works

- Enter the total number of items (n) and the number of items to choose (r).
- Select the combination type: 'Without Repetition' for distinct selections or 'With Repetition' for scenarios where items can be picked multiple times.
- Enable optional settings to view the mathematical formula, step-by-step derivation, or Pascal's triangle position.
- Click calculate to receive the result along with the detailed combinatorial analysis.

## Use cases

- Calculating lottery odds or card game hand possibilities.
- Determining the number of ways to form committees or teams from a group of people.
- Analyzing data distribution patterns in statistical research.

## Frequently asked questions

### What is the difference between combinations with and without repetition?

Without repetition means each item can be selected only once. With repetition allows the same item to be chosen multiple times.

### Does the order of selection matter in this calculator?

No, combinations specifically ignore the order of selection. If order matters, you should use a permutation calculator instead.

### What is the maximum value for n and r?

The calculator supports values for n and r up to 50.

### Can I see the formula used for the calculation?

Yes, by enabling the 'Show mathematical formula' option, the tool will display the specific formula applied to your inputs.

### What is the Pascal triangle position feature?

This feature identifies the specific row and column index where your combination result appears within Pascal's triangle.

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