Combinatorics Calculator

Calculate Permutations ($nPr$), Combinations ($nCr$), and Factorials ($n!$). Determine total possible arrangements and selections of items where order matters (permutations) or order does not matter (combinations).

Why Use This Tool?

• Probability & Statistics: Calculate probability odds and event combination outcomes.
• Lottery & Game Analysis: Compute total possible card combinations or lottery ticket selection odds.
• Computer Science & Algorithms: Calculate search space complexity for algorithms.

How to Use

1. Enter Total Items $n$ (e.g. `10`) and Selected Items $r$ (e.g. `3`).
2. Select Operation: Combination $nCr$ or Permutation $nPr$.
3. View calculated result and step-by-step formula solution.

Real Working Example

Input:

Total Items (n): 10 | Selected Items (r): 3 | Mode: Combination (nCr)

Output Result:

10C3 = 10! / (3! * 7!) = 120 unique combinations

Important Technical Details & Formulas

• Combination Formula: `nCr = n! / (r! * (n - r)!)`.
• Permutation Formula: `nPr = n! / (n - r)!`.
• BigInt Precision: Handles large factorials ($n!$) accurately without numeric overflow.

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