By combining a one-meson-exchange model for the Λ N → n N transition in finite nuclei with an intranuclear cascade code, we have obtained nucleon-nucleon (angular and energy) coincidence distributions from the nonmesonic weak decay of 5 Λ H e and 12 Λ C hypernuclei. Although, due to the elimination of interferences, two-nucleon coincidences are expected to give a cleaner extraction (with respect to single nucleon observables) of the ratio Γ n / Γ p ≡ Γ ( Λ n → n n ) / Γ ( Λ p → n p ) , we show that the effect of the final state interactions is still important even when applying favorable energy and angular cuts. The agreement of our results for the ratio N n n / N n p between the number of n n and n p emitted pairs with preliminary KEK coincidence data allows us to conclude that Γ n / Γ p for 5 Λ H e should be small and close to the value of 0.46 predicted by our meson-exchange model.