  $p\,\Lambda$ emission in coincidence following $K^-$ absorption at rest in
nuclei is studied using quantum mechanical scattering theory and nuclear wave
functions. $K^-$ absorption is assumed to occur on two protons in the nucleus.
In the formalism, emphasis is put on the study of the final state interaction
(FSI) effects of $p$ and $\Lambda$ with the recoiling nucleus. We include
elastic scattering and single nucleon knock-out (KO) channels in the FSI.
Calculations are presented for the $^{12}$C nucleus, using shell model wave
functions, and without any extra mass modification of the $K^-\,pp$ system in
the nucleus. Calculated results are presented for the angular correlation
distribution between $p$ and $\Lambda$, their invariant mass distribution and
the momentum spectra of $p$ and $\Lambda$. These results are compared with the
corresponding experimental measurements \cite{agnello}. With only elastic
scattering FSI included, the angular correlation distribution and the momentum
spectra are found to be in good accord with the corresponding measurements.
With full FSI the calculated $p\,\Lambda$ invariant mass distribution is found
to have two peaks, one corresponding to the elastic scattering FSI and another
to single nucleon KO FSI. The KO peak agrees fully, in position and shape, with
the peak observed in Ref. \cite{agnello}. The peak corresponding to elastic
scattering FSI does not seem to exist in the measured distribution. Considering
that such a two peak structure is always seen in the inclusive ($p$, $p^\prime
$) and ($e$, $e^\prime $) reactions in nuclei at intermediate energies, absence
of the elastic scattering peak in the $p\,\Lambda$ reaction is intriguing.
