二项式系数在数学上是二项式定理中的系数族。其必然为正整数，且能以两个非负整数为参数确定，此两参数通常以n和k代表，并将二项式系数写作，亦即是二项式幂(1 + x)的多项式展式中，x项的系数。如将二项式系数的n值顺序排列成行，每行为k值由0至n列出，则构成帕斯卡三角形。

此数族亦常见于其他代数学领域中，尤其是组合数学。任何有n个元素的集合，由其衍生出拥有k个元素的子集，即由其中任意k个元素的组合，共有个。故此亦常读作「n选取k」。二项式系数的特性使表达式的定义不再局限于n和k均为非负整数及k ≤ n，然此等表达式仍被称为二项式系数。

In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written . It is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x). Under suitable circumstances 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.