This page explains exactly how the Visual Combinatorics Calculator works — what runs locally in your browser,
how permutation and combination computations are handled, and what technologies power the site.
We aim for full transparency to ensure mathematical accuracy and user trust.
Privacy at a glance: All calculations occur directly in your browser.
We DO NOT store, log, or send your inputs or results to any external server.
1) Core Calculation Logic
Purpose: The calculator determines the total number of possible permutations and combinations
for a given set of elements, supporting both simple and advanced configurations — such as
with or without repetition, ordered or unordered selections, and linear or circular arrangements.
Note: No external mathematical or statistical libraries are used; all logic is custom-built for
precision and computational efficiency.
1.1 Implementation Summary
- All permutation and combination formulas are implemented using native C# arithmetic functions.
- Handles both repetition and non-repetition cases (e.g., arrangements where repetition is allowed).
- Provides step-by-step breakdowns for \( nPr \) and \( nCr \) formulas to enhance learning and understanding.
- Includes support for circular and distinct arrangements through extended combinatorial logic.
- Optimized for large-number calculations using safe integer overflow checks in .NET.
2) Types of Combinatorial Calculations
- Permutation (nPr): Calculates ordered arrangements where order matters.
- Combination (nCr): Calculates selections where order does not matter.
- Permutation with Repetition: Allows repeated elements within ordered arrangements.
- Combination with Repetition: Allows repeated selections from the same set.
- Multiset Combinations: Handles cases where elements may have duplicate counts.
- Circular Permutations: Determines distinct arrangements in circular order (accounting for rotations).
3) Visualization Methodology
Once calculations are completed, the results are displayed using responsive HTML and CSS elements.
No external JavaScript or graphics libraries are used — this lightweight and dependency-free implementation ensures instant responsiveness across all devices, from mobile phones to desktop systems.
4) Application Stack
Frontend: ASP.NET (Web Forms), HTML5, CSS3, JavaScript
Language: C#
Database: Microsoft SQL Server
Target Framework: .NET Framework
Note: No user-entered data or results are stored on the server.
5) Accessibility & UX Notes
- Input fields allow users to enter number of elements (n) and selection size (r),
along with repetition and arrangement options.
- High-contrast visuals and well-structured result blocks make mathematical outputs easy to read.
- Keyboard-accessible and mobile-responsive layout ensures accessibility for all users.
6) Security & Integrity
- All computations are performed locally — no personal data or calculation history is logged or transmitted.
- No cookies, session storage, or third-party analytics tied to calculation data.
- The website is protected via HTTPS and follows best practices for content integrity and safe browsing.
7) Accuracy and Validation
- All formulas implemented follow standard combinatorial mathematics principles.
- Each calculation result is cross-verified for integer precision and mathematical consistency.
- Error handling ensures invalid inputs (negative numbers, r > n, etc.) are safely managed.
Contact Us
Have questions or suggestions? Reach the Visual Combinatorics Calculator team through our
Contact Page.
We welcome feedback to improve clarity, precision, and educational value.