Plan samples using accurate n and r calculations. Review counts before audits, sorting, and testing. Get dependable results, exports, examples, and guidance in seconds.
| Scenario | n | r | Mode | Result |
|---|---|---|---|---|
| Incoming inspection units | 12 | 3 | Combination (nCr) | 220 |
| Audit checkpoint pairs | 10 | 2 | Combination (nCr) | 45 |
| Failure ranking order | 8 | 3 | Permutation (nPr) | 336 |
| Defect code grouping | 5 | 4 | Combination with Repetition | 70 |
Combination: nCr = n! / [r!(n - r)!]
Use this when order does not matter.
Permutation: nPr = n! / (n - r)!
Use this when order matters.
Combination with Repetition: (n + r - 1)Cr
Use this when the same category can appear more than once.
Quality teams often need to count possible sample selections. That is where an n pick r calculator helps. It shows how many ways a team can choose items from a batch. This matters in inspection planning, audit routing, defect review, and traceability work. A clear count reduces guesswork. It also helps teams explain why a sampling choice is reasonable.
In quality control, combinations are common. Use them when order does not matter. A set of five inspected units from a lot of fifty is a combination problem. Permutations matter when order changes the meaning. This can happen in step sequencing, ranked failure review, or rotating audit assignments. Repetition options matter when categories can repeat, such as defect codes or checklist tags.
This calculator supports all three views in one place. Enter n for the total available items. Enter r for the number selected. Then choose the mode that fits the task. The result section shows the exact count, scientific notation, and the formula used. That helps with reporting. It also supports fast peer review during process meetings.
A good n pick r workflow supports better sampling decisions. Teams can compare inspection depth before a lot moves forward. They can estimate how many sample groups are possible. They can also document why a plan is broad enough for the process risk. This is useful in incoming inspection, in process checks, final audits, and supplier quality reviews.
The calculator is also helpful during training. New inspectors can see how sample choices grow quickly as lot size changes. Supervisors can show why random selection rules should be documented. Engineers can compare selection counts before changing a control plan. Managers can attach the exported report to a corrective action file. That improves communication across departments. It also supports audit readiness and cleaner sampling documentation today.
Use the example table to test common scenarios. Export the result to CSV for records. Export the PDF summary for meetings or approvals. When people share the same numbers, discussions improve. That saves time. It also supports consistency across shifts, lines, and quality checkpoints. A simple counting tool can strengthen process control when the method is clear and repeatable.
It means selecting r items from n available items. The calculator can count choices when order matters, does not matter, or repeated categories are allowed.
Use combinations when the order of selected items does not change the result. This fits many inspection, audit, and sample selection tasks in quality control.
Use permutations when arrangement or sequence matters. This is useful for ranked checks, step ordering, rotating audit paths, or prioritized failure review.
Repetition means the same category or option can appear more than once in the selection. It helps with repeated defect classes, labels, or grouped checklist outcomes.
Selection counts grow quickly as n and r increase. Large values are normal in combinatorics, so the page also shows scientific notation and digit count.
Yes. It helps compare possible sample groups and explain lot selection logic. It does not replace formal standards, but it supports planning and documentation.
A zero or invalid result usually means the inputs break the selected rule. For example, r cannot exceed n for standard combinations or standard permutations.
The exports include the entered values, selected mode, formula label, exact result, scientific notation, and the example table so teams can save or share the calculation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.