Permutations & Combinations Calculator
Calculate the number of ways to arrange or select items from a set. Permutations care about order; combinations do not. Enter n and r to get both values.
Permutations vs Combinations
The Key Difference
Permutations: order matters. Choosing 1st, 2nd, 3rd from 10 people — ABC ≠ BAC. Combinations: order doesn't matter. Choosing 3 team members from 10 — ABC = BAC = CBA. nCr = nPr ÷ r!
Formulas
nPr = n! / (n−r)!. nCr = n! / (r! × (n−r)!). For large n, use logarithms to avoid overflow. Excel: PERMUT(n,r) and COMBIN(n,r). Python: math.perm(n,r) and math.comb(n,r).
Everyday Examples
Lottery (6 from 49): C(49,6) = 13,983,816 combinations. Lock combinations (4-digit with repetition): 10⁴ = 10,000. Team selection (5 from 20 players): C(20,5) = 15,504. Race results (top 3 from 8): P(8,3) = 336.
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