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.

Formula:
Examples: