LaTeX
\binom{n}{r}=\frac{n!}{r!(n-r)!}Variables
- n: total items
- r: selected items
How to use this formula
Counts unordered selections of r items from n distinct items.
Important notes
- Order does not matter.
Quick example
C(5,2)=10.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Order does not matter.
- For the Combination 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
C(5,2)=10.
Common mistakes
- When copying Combination 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 Combination 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
\binom{n}{r}=\frac{n!}{r!(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 Combination Formula used for?
Counts unordered selections of r items from n distinct items.
Can I copy this formula as LaTeX?
Yes. Copy \binom{n}{r}=\frac{n!}{r!(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.