Permutations (nPr) & Combinations (nCr)Mathematics

Permutations (nPr) and Combinations (nCr) Math Calculator

Calculate permutations with order nPr, combinations without order nCr, and factorials n! for advanced probability and combinatorics calculations.

Calculator Inputs

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Calculated ResultPermutations (nPr) & Combinations (nCr)

Combinations (nCr Without Order)

120ways

Permutations (nPr With Order)

720 ways

Factorial of Selection (r!)

6 permutations

Exact Combinatorics: Highlights the multiplying power of positional ordering.

Permutations vs Combinations

Combinations nCr
120 ways(14%)
Permutations nPr
720 ways(86%)

Detailed Calculation Breakdown

Internal Orderings (r!)
6 ways
Combinations nCr
120 ways
Permutations nPr
720 ways

Calculation Methodology

Permutation: nPr = n! / (n - r)!. Combination: nCr = n! / [r! * (n - r)!], where n is total elements and r is sample size.

Important Legal & Educational Disclaimer

This discrete mathematics tool computes exact combinatoric permutations and subsets.

This calculator is designed for educational and informational purposes only based on public statutory frameworks. The outputs do not constitute binding financial, tax, or legal advice. We assume no liability for decisions made based on these estimations. Always verify with the relevant official authorities or a certified professional advisor.

Frequently Asked Questions

Use Permutations when order matters (e.g., race podium rankings); use Combinations when selection order does not matter (e.g., lottery numbers).
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