binomial coefficient

A binomial coefficient is any of the coefficients of the powers of x or y in the expansion (see binomial theorem) of (x + y)n.


The binomial coefficient of a typical term x(n - m)ym, written nCm, or (mn), gives the number of ways of picking m unordered outcomes from n possibilities, and is also known as a combination. It has the value n!/(n - m)!m!


The binomial coefficients form the rows of Pascal's triangle.