Probability, Permutation & Combination Calculator

Calculate event probabilities, combinations (nCr), and permutations (nPr)

Total Set (n)

Items Selected (r)

Calculation Result

Combinations nCr (Order doesn't matter)

120

Permutations nPr (Order matters): 720

Combinations (nCr)

120

Permutations (nPr)

720

Formula

n! / (r!(n-r)!)

Input total items (n) and items chosen (r).

Calculate total unique permutations and combinations.

Combinatorics Formulas

nPr = n! / (n - r)!; nCr = n! / [r! × (n - r)!]

Permutations count ordered arrangements, while combinations count selections where order does not matter.

n = 10, r = 3.

• Combinations (10C3) = 10! / (3! × 7!) = (10 × 9 × 8) / 6 = 120

• Permutations (10P3) = 10 × 9 × 8 = 720

There are 120 combinations and 720 ordered permutations.

In permutations (nPr), order matters (like a passcode). In combinations (nCr), order does not matter (like a hand of cards).

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