  In the framework of the color-magnetic interaction, we have systematically
studied the mass splittings of the possible hidden-charm pentaquarks
$qqqc\bar{c}$ ($q=u,d,s$) where the three light quarks are in a color-octet
state. We find that i) the LHCb $P_c$ states fall in the mass region of the
studied system; ii) most pentaquarks should be broad states since their
$S$-wave open-charm decays are allowed while the lowest state is the
$J^P=\frac12^-$ $\Lambda$-like pentaquark with probably the suppressed
$\eta_c\Lambda$ decay mode only; and iii) the $J^P=\frac52^-$ states do not
decay through $S$-wave and their widths are not so broad. The masses and widths
of the two LHCb $P_c$ baryons are compatible with such pentaquark states. We
also explore the hidden-bottom and $B_c$-like partners of the hidden-charm
states and find the possible existence of the pentaquarks which are lower than
the relevant hadronic molecules.
