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Step log
Steps are hidden. Turn on “Show steps” to view them.
FAQ
What is the difference between permutations and combinations?
Permutations treat the order of selection as unique (AB ≠ BA). Combinations treat those as the same outcome, counting only distinct subsets.
When should I switch between Exact and Approx?
Use Exact for values within the BigInt range (up to about n = 10,000 with k ≤ 5,000). Switch to Approx when the exact integer would be too large; you will still see the digit count and an accurate scientific notation.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.
How to use nCr & nPr effectively
Choose nCr, nPr, or factorial
Use nCr when order does not matter, such as choosing 3 winners from 10 people. Use nPr when order matters, such as assigning 1st, 2nd, and 3rd place. Use n! when arranging all items.
Worked examples
- Lottery-style selection: choosing 6 numbers from 49 is a combination because 1-2-3-4-5-6 is the same ticket in any order.
- Seating or ranking: arranging 5 finalists in 3 ordered slots is a permutation because each slot has a different meaning.
- Large values: switch to Approx when the exact integer is too large, then use digit count and scientific notation for scale.
Use the step log for learning
The step log shows multiplication and division in a stable order. Teacher mode adds symmetry hints such as C(n,r)=C(n,n-r), which helps reduce work and catch impossible inputs.
Common mistakes to avoid
- Using nPr when the selected set has no ranking or order.
- Forgetting that
rmust be between 0 andn. - Comparing approximate scientific notation with an exact integer without checking digit count.
How it’s calculated