  We present a new method of solving the probability distribution for baryons,
antibaryons and mesons at the hadronization of constituent quark and antiquark
system. The hadronization is governed by the quark combination rule in the
quark combination model developed by the Shandong Group. We use the method of
the generating function to derive the outcome of the quark combination rule,
which is much simpler and easier to be generalized than the original method.
Furthermore, we use the formula of the quark combination rule and its
generalization to study the property of multiplicity distribution of
net-protons. Taking a naive case of quark number fluctuations and correlations
at hadronization, we calculate ratios of multiplicity cumulants of final-state
net-protons and discuss the potential applicability of quark combination model
in studying hadronic multiplicity fluctuations and the underlying phase
transition property in relativistic heavy-ion collisions.
