The analytic solution of the polymer Percus-Yevick approximation for the multicomponent version of the totally flexible sticky two-point model of Wertheim is obtained in closed form. The model consists of an n-component mixture of hard spheres with two sticky points of the type A and B randomly placed on the surface of each hard sphere. The solution of the problem has been reduced to solving a set of 5n algebraic equations. An iterative scheme of the solution of this set of equations is proposed.