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Binomial Coefficients in Pascal's Triangle

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

These numbers, called binomial coefficients because they are used in the binomial theorem, refer to specific addresses in Pascal's triangle. They refer to the nth row, rth element in Pascal's triangle as shown below.

The formula used to compute binomial coefficients directly is found below as well.

 

refers to the nth row, rth element in Pascal's Triangle.  
Example:

is the 5th row, 4th element, so

5C4 is another notation for the same element.

 

Formula:
Examples:

 


  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