KEVOS® MAKEOS · Mathematics
Factorials, Permutations and Combinations
How many arrangements or selections of r items from n are possible?
Factorial n!, permutations nPr and combinations nCr, with large values in scientific notation, for sampling plans, tooling options and probability.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Total items n | items | Number of distinct items available (up to 170). |
| Items chosen r | items | Number of items chosen. |
Method and formulas
- n! = 1 × 2 × … × n (0! = 1).
- nPr = n! ÷ (n − r)!.
- nCr = n! ÷ (r! (n − r)!).
- Example: from 10 items, 3 can be arranged in 720 ways and chosen in 120 ways.
Limitations
- Values beyond about 10¹⁵ are shown in floating point and are approximate in the last digits.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Count possible tool or set-up combinations
- Support sampling and probability calculations
- Check combinatorics in test plans
Who it is for
- Engineers
- Technicians
- Engineering students
What you get
- n!
- Permutations nPr (order matters)
- Combinations nCr (order does not matter)
Interpreting the result
- Use combinations when order does not matter, permutations when it does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 19. Topic reference; no source tables or recommended settings are reproduced.
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