A detailed quantitative study of the pnictide composite superconductor (CS) Ba_0.6K_0.4Fe₂As₂ is presented in the frame-work of the recently derived set of generalized BCS equations. Invoking multiple Debye temperatures to take into account anisotropy of the CS, we address the current experimental data on its T_c and the (not so clear-cut) gap-values via different theoretical scenarios that attempt to identify the ion species responsible for pairing in it. This is done with the aid of the Bogoliubov’s restriction on the BCS dimensionless electron-phonon coupling constant. Significantly, our study sheds light on the gaps which have recently been observed in different iron-pnictide CSs as nodes or line-nodes on the Fermi surface and have evinced considerable interest.