In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written . It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n. The value of the coefficient is given by the expression . Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle. The binomial coefficients occur in many areas of mathematics, especially in the field of combinatorics. is often read aloud as "n choose k", because there are ways to choose a subset of size k elements, disregarding their order, from a set of n elements. The properties of binomial coefficients have led to extending the definition to beyond the common case of integers n ≥ k ≥ 0.

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