The calculation, without hidden assumptions
Counting problems usually fail at one decision before the arithmetic even starts: does order matter? This owner computes nCr and nPr side by side with exact integer arithmetic, so you can compare selection versus arrangement without bouncing between two near-duplicate pages.
How to use this calculator
Enter the total number of distinct items n and the number selected r.
Read nCr for unordered selections and nPr for ordered arrangements.
Use the visible formulas to decide which count belongs in your probability or counting problem.
Where people use it
- •Probability and statistics homework
- •Counting teams, committees or lottery selections
- •Counting ordered arrangements, rankings or codes without replacement
Example: choose or arrange 2 from 5
Choosing 2 people from 5 gives C(5,2)=10 because AB and BA are the same pair. Arranging 2 from 5 gives P(5,2)=20 because AB and BA are different orders.
What the result does not assume
- •This owner assumes distinct items and selection without replacement. Repetition/multiset counting is a different model.
- •Inputs are limited to practical exact-integer ranges to keep browser output responsive.
Frequently asked questions
What is the difference between nCr and nPr?+
nCr ignores order; nPr counts different orders as different outcomes.
Are large results rounded?+
No. The calculator uses exact integer arithmetic for nCr and nPr within the supported input range.
Does this allow repeated selections?+
No. It models choosing or arranging distinct items without replacement.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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