How to use the Permutation and Combination Calculator
Estimate combinations from total amount in a set (n), amount in each sub-set (r) with the Permutation and Combination Calculator. It includes Combination, Permutation, Permutation with repetition workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.
Step by step
- For the Permutation and Combination example, select Combination and enter total amount in a set (n), amount in each sub-set (r). Keep each value in the unit displayed beside its field.
- Review the selected Permutation and Combination workflow and inputs, then read combinations in the result panel.
- Change one Permutation and Combination assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.
How the calculation works
Uses nCr when order does not matter, nPr for ordered selections without reuse, and n^r for ordered selections with repetition.
Worked example
To reproduce the Permutation and Combination worked example, reset the calculator. Select the Combination workflow. Use total amount in a set (n) 10; amount in each sub-set (r) 3. The result is combinations of 120. Exact integer result computed without floating-point rounding. Review the displayed units before comparing the result.
Understanding the result
The Permutation and Combination reports combinations. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.
How to check the answer
Check the Permutation and Combination answer by substituting combinations back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Uses nCr when order does not matter, nPr for ordered selections without reuse, and n^r for ordered selections with repetition.
Common questions
What does the Permutation and Combination calculate?
Estimate combinations from total amount in a set (n), amount in each sub-set (r) with the Permutation and Combination Calculator.
Which inputs does the Permutation and Combination example use?
The worked example uses total amount in a set (n), amount in each sub-set (r) in the Combination workflow. Other workflows can show different fields. Keep the chosen workflow and units with the result when comparing calculations.
Is the Permutation and Combination result exact?
The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck total amount in a set (n), amount in each sub-set (r) and use combinations only for a decision where that level of precision is appropriate.