When to use this calculator
Count handshakes or unique pairings among distinct participants. Each pair is counted once; self-pairs are excluded.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Permutation Calculator: Count ordered selections without replacement.
PUTTING IT INTO PRACTICE
Pair Count: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Distinct participants (integer) | 10 |
| Result | 45 pairs |
- Check the input labels and enter the example values above.
- Apply the relationship: Unordered pairs = n(n−1)/2.
- The result is 45 pairs, rounded for display.
How to interpret your result
Each pair is counted once; self-pairs are excluded.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the pair count calculator useful?
Count handshakes or unique pairings among distinct participants. Each pair is counted once; self-pairs are excluded.
How do I use the pair count calculator?
Enter distinct participants (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Unordered pairs = n(n−1)/2.
What should I check before using the result?
Each pair is counted once; self-pairs are excluded.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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