The aim of this paper is to calculate the binary and triplet distribution functions for one and two component Plasmas in terms of Green's function technique. We obtained the triplet distribution function in two form; one of them is based on the Kirkwood Superposition Approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three binary distribution functions, but the other form is calculated from BBGKY hierarchy.