About Unique Set Counting
Unique sets, combinations, and permutations describe different counting tasks. A set ignores order. A permutation respects order. A repeated arrangement allows the same item to appear again. A duplicate-aware count removes repeated copies that would otherwise inflate the answer.
Why This Calculator Helps
Many real problems mix these ideas. A password rule may allow repeats. A team selection does not care about order. A word arrangement may contain duplicate letters. A sample draw may exclude unavailable items. This calculator keeps those cases separate, so the final numbers are easier to compare.
Core Counting Ideas
Use combinations when position does not matter. Use permutations when first, second, and later positions are different. Use repeated combinations when an item can be chosen more than once, but order still does not matter. Use repeated permutations when every slot can accept any available item.
Duplicate Groups
Duplicate groups are useful for words, cards, inventory lots, and coded labels. Enter values such as 2,2,3 when three groups contain equal copies. The calculator treats those repeated copies as indistinguishable. It then divides the total arrangement count by each duplicate factorial.
Effective Item Count
The effective total equals the original item count minus exclusions. Exclusions represent removed symbols, unavailable players, blocked choices, or reserved objects. The chosen size should not exceed the effective total for non-repeating selections. Repeating modes can still work with a larger chosen size.
Interpreting Results
Large counts can grow very quickly. The calculator shows exact values when practical. It also uses scientific notation when results become very large. This keeps the page readable while preserving a useful scale. Use the CSV export for spreadsheets. Use the PDF export for quick reports.
Practical Uses
Teachers can compare formulas in one place. Students can check homework steps. Analysts can estimate possible product bundles. Game designers can count deck, loot, or build options. Event planners can compare seating orders and committee choices. The examples table gives a fast starting point for testing.
Clean Export Workflow
After calculating, review the summary first. Then save the CSV for deeper sorting. Save the PDF when you need a printable snapshot with formulas, inputs, and final values shown together for later review and sharing.