🔄 Permutations & Arrangements Calculator
Find the number of ordered arrangements for different scenarios: distinct items (nPr), repeated characters (multiset permutations), and circular arrangements. Supports large inputs via log-gamma approximations and exact BigInt factorials where feasible.
1. Distinct Elements (nPr)
Calculate ordered selections without repetition.
Permutations
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2. Permutations with Repeated Characters
Ideal for words like “BANANA” (3 A’s, 2 N’s, 1 B).
Unique permutations
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Includes scientific notation for extremely large results.
3. Circular Arrangements
Arranging items around a round table or ring.
Circular permutations
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Uses exact factorial up to n=171, switches to scientific notation beyond.
How to Use
- Choose the appropriate panel (distinct nPr, repeated characters, or circular arrangements) for your problem.
- Provide integer inputs: n and r for nPr, counts of repeated elements for multiset permutations, or the number of distinct items for circular arrangements.
- Run the calculation to see exact results where feasible; the tool switches to scientific notation when values exceed floating-point limits.
- Watch for warning messages if totals and counts conflict, and use the reset buttons to clear inputs when starting a new example.
Formula References
- Tucker, A. (2002). Applied Combinatorics (5th ed.). Wiley.
- Rosen, K. H. (2012). Discrete Mathematics and Its Applications (7th ed.). McGraw-Hill.