Permutation (nPr) & Combination (nCr) Calculator
Determine the number of possible arrangements and groupings for any set of items. Calculate permutations where order matters (nPr) and combinations where order does not matter (nCr) with clear factorial step-by-step explanations.
How to Use Permutation & Combination Calculator (nPr & nCr)
Enter Total Items (n)
Input the total number of items in the set (n ≥ 0).
Enter Items Taken (r)
Input the number of items selected in each subset (r ≤ n).
Select Mode
Choose Without Repetition (standard) or With Repetition permitted.
About Permutation & Combination Calculator (nPr & nCr)
The fundamental distinction between permutations and combinations is whether order matters. A combination lock is technically a 'permutation lock' because the sequence 1-2-3 is distinct from 3-2-1. In a lottery drawing, order does not matter, making it a combination.
Key Features
- Permutations Formula: nPr = n! / (n - r)!
- Combinations Formula: nCr = n! / [r! × (n - r)!]
- Permutations with Repetition: n^r
- Combinations with Repetition: (n + r - 1)! / [r! × (n - 1)!]
- Step-by-step factorial cancellation breakdown
Frequently Asked Questions
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