Probability

Permutations

Formula

P(n, r) = n! / (n−r)!

What is Permutations?

Permutations count the number of ways to arrange r items from n items where order matters. Each different ordering counts as a separate permutation.

Variables

n
n — Total number of items
r
r — Number of items to arrange
!
! — Factorial (e.g., 5! = 5×4×3×2×1)

Worked Examples

Example 1

How many ways can 3 people sit in 5 chairs?

Solution:

P(5,3) = 5! / 2! = 120 / 2 = 60

Frequently Asked Questions

Related Formulas

P(Event) = (Number of favorable outcomes) / (Total number of outcomes)

C(n, r) = n! / (r! × (n−r)!)

Binomial Probability

P(X = k) = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ

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