Permutations Calculator

Compute permutations \( P(n, k) \) and permutations with repetition effortlessly.

Permutations Solver

Enter the total items (\( n \)) and items to arrange (\( k \)) to calculate permutations.

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k
About Permutations

Permutations count the number of ways to arrange \( k \) items from \( n \) items where order matters. The standard formula is:

  • \( P(n, k) = \frac{n!}{(n - k)!} \)
  • For repetition: \( P(n, k) = n^k \)

Examples:

  • Race Podium: How many ways to arrange 3 runners from 5 for 1st, 2nd, 3rd? \( P(5, 3) = \frac{5!}{(5-3)!} = \frac{120}{2} = 60 \). Answer: 60 ways.
  • Password Creation: How many 3-digit codes from 4 digits (repetition allowed)? \( P(4, 3) = 4^3 = 64 \). Answer: 64 codes (e.g., 111, 112, etc.).
  • Seating Arrangement: How many ways to seat 2 people from 4 in 2 chairs? \( P(4, 2) = \frac{4!}{(4-2)!} = \frac{24}{2} = 12 \). Answer: 12 ways.