C-12.1 binomial coefficients are a family of positive integers that have a number of useful properties and they can be defined in several ways. one way to define them is as an indexed recursive function, c(n, k), where the “c” stands for “choice” or “combinations.” in this case, the definition is as follows: c(n, 0) = 1, c(n, n)=1, and, for 0