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The electron target asymmetries A || and A ⊥ with target spin parallel and perpendicular to the momentum transfer were measured for both the two- and three-body breakup of 3He in the 3 (¯e, e’p)-reaction. Polarized electrons were scattered off polarized 3He in the quasielastic regime in parallel kinematics with the scattered electron and the knocked-out proton detected using the Three-Spectrometer Facility at MAMI. The results are compared to Faddeev calculations which take into account Final-State Interactions as well as Meson Exchange Currents. The experiment confirms the prediction of a large effect of Final-State Interactions in the asymmetry of the three-body breakup and of an almost negligible one for the two-body breakup.