We discuss the reaction of associated production of a top quark pair and a Higgs boson at the future e⁺ e^- linear collider that can be used to determine the top-Higgs Yukawa coupling. Taking into account decays of the top quarks and the light Higgs boson leads to reactions with 8 fermions in the final state which, in the framework of the Standard Model, receive contributions typically from many thousands Feynman diagrams. An overwhelming majority of the diagrams comprises the off resonance background to the resonant signal of associated production and decay of the top quark pair and Higgs boson. We address the signal and background issue by comparing cross-sections calculated with the signal diagrams only and with the complete sets of the diagrams.

PACS numbers: 14.65.Ha, 14.80.Bn