It is a standard textbook exercise to show that by considering the coefficients of xn first in (1 + x)n. (1 + x)n and then in (1 + x)2n It is the purpose of this note to show that formulas for a wide class of sums of products of binomial coefficients can be obtained by using Leibniz’ rule for the differential coefficient of a product; all expressions are derived for three indices, but generalization to any other number is obvious.