Permutations calculate the number of ways to arrange k items from n items where order matters.
⚠Values limited to n ≤ 20 to prevent overflow. For larger values, use logarithms or scientific notation.
What is Permutation?
A permutation is an arrangement of all or part of a set of objects where the order of arrangement matters. For example, arranging letters A, B, C: ABC, ACB, BAC, BCA, CAB, CBA are all different permutations.
Order Matters
AB ≠ BA - different arrangements count as different permutations
Formula
P(n,k) = n! / (n-k)! where n ≥ k ≥ 0
Factorial
n! = n × (n-1) × ... × 1, with 0! = 1
Full Permutation
P(n,n) = n! - arranging all items
💡 Example: P(5,3) = 5! / (5-3)! = 120 / 2 = 60. There are 60 ways to arrange 3 items from 5.
A permutation is an arrangement of all or part of a set of objects where order matters. P(n,k) = n! / (n-k)! where n is total items and k is items to arrange.
What is the difference between permutation and combination?▼
Permutation: order matters (AB ≠ BA). Combination: order does not matter (AB = BA). P(n,k) = n!/(n-k)! and C(n,k) = n!/(k!(n-k)!).
What is factorial?▼
Factorial of n (written n!) is the product of all positive integers up to n. n! = n × (n-1) × (n-2) × ... × 1. By definition, 0! = 1.
When would I use permutations?▼
Use permutations when order matters: arranging people in a line, selecting a president/vice-president, arranging letters, or any ordered selection.
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