  The $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ observed by the LHCb
Collaboration are very likely to be $S$-wave $\Sigma_c\bar{D}^{(*)}$ molecular
candidates due to their near-threshold character. In this work, we study the
hidden-charm decay modes of these $P_c$ states, $P_c\to J/\psi p(\eta_cp)$,
using a quark interchange model. The decay mechanism for the $P_c\to J/\psi
p(\eta_cp)$ processes arises from the quark-quark interactions, where all
parameters are determined by the mass spectra of mesons. We present our results
in two scenarios. In scenario I, we perform the dynamical calculations and
treat the $P_c$ states as pure $\Sigma_c \bar D^{(*)}$ molecules. In scenario
II, after considering the coupled channel effect between different flavor
configurations $\Sigma^{(*)}_c\bar D^{(*)}$, we calculate these partial decay
widths again. The decay patterns in these two scenarios can help us to explore
the molecular assignment and the inner flavor configurations for the $P_c$
states. In particular, the decay widths of $\Gamma(P_c(4312)\to\eta_cp)$ are
comparable to the $J/\psi p$ decay widths in both of these two scenarios.
Future experiments like LHCb may confirm the existence of the $P_c(4312)$ in
the $\eta_cp$ channel.
