Quick Start
First, visit the Permutation (排列数) tool on HeronTool. Enter the total number of elements n and selection count r, then click 'Calculate' to get the permutation count P(n,r) = n!/(n-r)!. For example, choosing 3 from 5 elements gives 60 permutations. The tool also lists all possible sequences.
Using Combination Tool
For scenarios where order doesn't matter, use the Combination (组合数) tool. Similarly input n and r, click calculate to get C(n,r) = n!/[r!(n-r)!]. For example, choosing 3 from 5 gives 10 combinations. The tool displays each combination's element set for verification.
Practical Tips
- If r=0 or r=n, the result is 1; the tool handles these boundaries automatically.
- Use the 'Swap' button to quickly exchange n and r values.
- For large n, results may overflow; the tool shows scientific notation.
- Combine with other HeronTool math tools (e.g., factorial) for advanced validation.
FAQ
Q: What's the difference between permutation and combination? Permutations consider order, combinations do not. For example, selecting a captain (permutation) vs. selecting team members (combination) differ.
Q: What if I input negative or decimal numbers? The tool shows an error; only non-negative integers are accepted.
Q: Can I generate all permutations or combinations? Yes, the tool offers an option to display all lists, limited to reasonable counts (e.g., total elements ≤ 10).
Q: Are results consistent with other calculators? Yes, formulas are standard; feel free to rely on them.
