LaTeX
P(n,r)=\frac{n!}{(n-r)!}Variables
- n: total items
- r: selected positions
How to use this formula
Counts ordered selections of r items from n distinct items.
Important notes
- Order matters and sampling is without replacement.
Quick example
P(5,2)=20.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Order matters and sampling is without replacement.
- For the Permutation Formula, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
P(5,2)=20.
Common mistakes
- When copying Permutation Formula, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not assume events are independent or mutually exclusive unless the problem states or proves that condition.
Continue the workflow
Use Permutation Formula in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
P(n,r)=\frac{n!}{(n-r)!}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Permutation Formula used for?
Counts ordered selections of r items from n distinct items.
Can I copy this formula as LaTeX?
Yes. Copy P(n,r)=\frac{n!}{(n-r)!} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.