Combination Calculator

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

Key Facts

Category: Math & Numbers
Input Types: number, select, checkbox
Output Type: json
Sample Coverage: 0
API Ready: Yes

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.

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.

Examples

1. Forming a Committee

Project Manager

Background: A manager needs to select a 3-person committee from a team of 10 employees.
Problem: Calculate how many unique committee combinations are possible.
How to Use: Set n=10, r=3, and select 'Without Repetition'.
Example Config: n=10, r=3, type=without_repetition
Outcome: The tool returns 120 possible unique committee combinations.

2. Selecting Ice Cream Flavors

Student

Background: A student is buying a 3-scoop bowl of ice cream from 10 available flavors, where flavors can be repeated.
Problem: Find the total number of flavor combinations possible with repetition allowed.
How to Use: Set n=10, r=3, and select 'With Repetition'.
Example Config: n=10, r=3, type=with_repetition
Outcome: The tool calculates 220 possible combinations for the ice cream bowl.

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FAQ

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.

API Documentation

Request Endpoint

POST /en/api/tools/combination-calculator

Request Parameters

Parameter Name	Type	Required	Description
n	number	Yes	-
r	number	Yes	-
type	select	Yes	-
showFormula	checkbox	No	-
showSteps	checkbox	No	-
showPascalTriangle	checkbox	No	-

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}

JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration:

{
  "mcpServers": {
    "elysiatools-combination-calculator": {
      "name": "combination-calculator",
      "description": "Calculate combinations (C(n,r)) with support for different types: with/without repetition, binomial coefficients, and detailed combinatorial analysis.",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=combination-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]

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