We use a relativistic model of meson-exchange currents to compute the proton-neutron and proton-proton yields in $(e,e)$ scattering from $^{12}$C in the 2p-2h channel. We compute the response functions and cross section with the relativistic Fermi gas model for a range of kinematics from intermediate to high momentum transfers. We find a large contribution of neutron-proton configurations in the initial state, as compared to proton-proton pairs. The different emission probabilities of distinct species of nucleon pairs are produced in our model only by meson-exchange currents, mainly by the $Delta$ isobar current. We also analyze the effect of the exchange contribution and show that the direct/exchange interference strongly affects the determination of the np/pp ratio.
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