🔢 Combinatorics Tool
Permutation & Combination Calculator
nPr · nCr · Factorial
Calculate permutations (nPr) and combinations (nCr) using factorial formula. Step-by-step breakdown included.
permutation calculator
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nPr
nCr
Calculator
n (total items) 10
r (selected items) 4
Permutations (nPr)
—
ordered arrangements
Combinations (nCr)
—
unordered selections
🧮 Step-by-step calculation
Enter n and r (n ≥ r ≥ 0) to see detailed factorial expansion.
📐 Formulas Used
🔹 nPr = n! / (n − r)!
🔹 nCr = n! / (r! × (n − r)!)
🔹 0! = 1
Permutation counts ordered arrangements; combination counts unordered selections. Valid when n ≥ r ≥ 0.