How to Use the Permutation & Combination (nPr & nCr) Calculator
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1
Enter total items $n$ and items chosen $r$ (where $0 \le r \le n$).
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2
The calculator computes Permutations $nPr = \frac{n!}{(n-r)!}$ (order matters).
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3
The calculator computes Combinations $nCr = \binom{n}{r} = \frac{n!}{r!(n-r)!}$ (order does not matter).
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4
Review the step-by-step factorial cancellation breakdown and Pascal's Triangle row values.
Practical Example & Use Case
Common Real-World Scenario
Calculating the number of possible 5-card poker hands from a 52-card deck: `52C5 = 2,598,960 combinations`.
Technical Notes & Limitations
Browser Engine Architecture
Uses JavaScript BigInt to compute factorials accurately beyond 100! without overflow.
Frequently Asked Questions
What is the fundamental difference between nPr and nCr?
Permutations ($nPr$) are used when the order of selection matters (e.g. combination locks, race podiums); Combinations ($nCr$) are used when order does not matter (e.g. lottery picks, committees).