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Binomial Coefficients

Numbers written in any of the ways shown below. Each notation is read aloud "n choose r."

A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal's triangle. These numbers are called binomial coefficients because they are coefficients in the binomial theorem.

 

Formula:
  Note: , where nPr is the formula for permutations of n objects taken r at a time.
Examples:

 


 

See also

Factorial, binomial coefficients in Pascal's triangle, combination formula, permutations

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes