Permutation & Combination Calculator
Calculate nPr (permutations) and nCr (combinations) with arbitrary precision BigInt factorials and arrangement listings.
Permutations (nPr)
720
Combinations (nCr)
120
Probability Analysis
Odds of specific Permutation:1 / 720(1.3889e-3%)
Odds of specific Combination:1 / 120(8.3333e-3%)
Step-by-Step Formulas
Permutation nPr
Formula: P(n, r) = n! / (n - r)!
Product Sequence: 10 × 9 × 8 = 720
Combination nCr
Formula: C(n, r) = n! / ((n - r)! × r!)
Calculation: P(10, 3) / 3!
= 720 / 6 = 120
Permutations vs. Combinations
A permutation counts arrangements where order matters: P(n,r) = n! / (n-r)!. A combination counts selections where order does not matter: C(n,r) = n! / ((n-r)! x r!). For C(n,r), this calculator uses BigInt arithmetic to calculate the exact factorials without losing precision, allowing exact results up to n=500.
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