# 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)}*y ^{m}*,
written

_{n}

*C*

_{m}, or (

^{m}

_{n}), 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.