  We study the possibly-existing molecular pentaquark states with open charm
and bottom flavors, {\it i.e.}, the states with the quark contents
$c\bar{b}qqq$ and $b\bar{c}qqq$ ($q=u,d,s$). We investigate the meson-baryon
interactions through the coupled-channel unitary approach within the local
hidden-gauge formalism, and extract the poles by solving the Bethe-Salpeter
equation in coupled channels. These poles qualify as molecular pentaquark
states, which are dynamically generated from the meson-baryon interactions
through the exchange of vector mesons. Our results suggest the existence of the
$\Sigma_c^{(*)} B^{(*)}$ and $\Sigma_b^{(*)} \bar{D}^{(*)}$ molecular states
with isospin $I=1/2$, the $\Xi_c^{(\prime,*)} B^{(*)}$ and $\Xi_b^{(\prime,*)}
\bar{D}^{(*)}$ molecular states with isospin $I=0$ and $I=1$, as well as the
$\Omega_c^{(*)} B^{(*)}$ and $\Omega_b^{(*)} \bar D^{(*)}$ molecular states
with isospin $I=1/2$.
