  We propose a novel method to extract the prompt neutron multiplicity
distribution, $P(\nu)$, in fission reactions based on correlations between
prompt neutrons, $\gamma$ rays, and fragment kinetic energy arising from energy
conservation. In this approach, only event-by-event measurements of the total
$\gamma$-ray energy released as a function of the total kinetic energy (TKE) of
the fission fragments are performed, and no neutron detection is required.
Using the $\texttt{CGMF}$ fission event generator, we illustrate the method and
explore the accuracy of extracting the neutron multiplicity distribution when
taking into account the energy resolution and calibration of the energy
measurements. We find that a TKE resolution of under 2 MeV produces reasonably
accurate results, independent of typical $\gamma$-ray energy measurement
resolution.
