Recent inverse-kinematics experiments with nuclear beams and proton target in GSI, RIKEN, and JINR aim to study the quenching of single-particle strength and the short-range NN correlations (SRC) in light nuclei. The new and important feature is the possibility to detect the outgoing nucleus in certain quantum states, which is quite challenging for nuclear structure models. The calculational framework for description of exclusive nucleon knockout reactions on 1p-shell nuclei has been developed. This includes the translationally invariant shell model of nuclear structure for the spectroscopic amplitude and the reaction model based on the DWIA. A good description of the GSI data for the ¹²С(р, pp)¹¹В process at 400A MeV is reached. Calculations were also performed for reactions ¹²С(р, ppn)¹⁰В and ¹²С(р, ppp)¹⁰Вe with carbon beam at 48 GeV/s, measured by the BM@N Collaboration at JINR to get information about SRC.