  The ratio N_{nn}/N_{np} between the number of neutron-neutron and
neutron--proton pairs emitted in the non--mesonic weak decay of
\Lambda-hypernuclei is calculated within a nuclear matter formalism extended to
^{12}_{Lambda}C via the local density approximation. The single--nucleon
emission spectra, N_p and N_n, are also evaluated. Our formalism takes care of
both ground state correlations (gsc) and final state interactions (FSI). The
evaluation of N_{nn}/N_{np} which, unlike Gamma_n/Gamma_p = Gamma(Lambda n ->
nn)/Gamma(Lambda p -> np), is an actual observable quantity in non--mesonic
decay is performed within a fully microscopic model where a proper treatment of
FSI, gsc and ground state normalization is considered. All the isospin channels
contributing to one-- and two--nucleon induced decays are included. Our final
result for the coincidence number ratio, N_{nn}/N_{np}=0.374, is in agreement
with the KEK--E508 datum, (N_{nn}/N_{np})^{\rm exp}=0.40 +/- 0.10.
