Practical tools for measured work
Probability and combinations calculator
Calculate equally likely probabilities, exact combinations and binomial event probability.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
How it works
For equally likely outcomes, probability = favourable / total. Combinations count unordered selections without replacement: n! / (k!(n−k)!). Binomial probability is C(n,k)p^k(1−p)^(n−k). With 10 independent fair trials, exactly 5 successes has probability 252/1024.
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Probability model
- Combinations and binomial probability
- Trials or items n
- 10
- Successes or choices k
- 5
- Success probability per trial
- 0.5
Primary result: Combinations n choose k: 252.
Before using the result
- Check the selected mode, units and input values before using the result.
- Read the assumptions and rounding rules; compare the worked example with your intended calculation.
- A numerical result does not supply missing context or change the stated limitations.
Limitations
Binomial trials must be independent with the same success probability. Use whole n from 0 to 1000 and k from 0 to n; probability must lie between 0 and 1. Extremely small probabilities can round or underflow to zero. Combination counts remain exact.
Frequently asked questions
Are the displayed decimals exact?
Fractions, combinations and integer multiples use exact integer arithmetic. Other results use floating-point arithmetic and are rounded for display. Keep the exact fraction when a repeating decimal matters.
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