  We apply an equal-velocity quark combination model to study the production of
light-flavor hadrons and single-charmed hadrons at midrapidity in $pp$
collisions at $\sqrt{s}=5.02$ TeV. We find experimental data for $p_{T}$
spectra of $\Omega$ and $\phi$ exhibit a quark number scaling property, which
is a clear signal of quark combination mechanism at hadronization. Experimental
data for $p_T$ spectra of $p$, $\Lambda$, $\Xi$, $\Omega$, $\phi$ and $K^{*0}$
are systematically described by the model. The non-monotonic $p_{T}$ dependence
of $\Omega/\phi$ ratio is naturally explained and we find it is closely related
to the shape of the logarithm of strange quark $p_{T}$ distribution. Using
$p_{T}$ spectra of light-flavor quarks obtained from light-flavor hadrons and a
$p_T$ spectrum of charm quarks which is consistent with perturbative QCD
calculations, the experimental data for differential cross-sections of
$D^{0,+}$, $D_{s}^{+}$ and $\Lambda_{c}^{+}$ as the function of $p_{T}$ are
systematically described. We predict the differential cross-sections of
$\Xi_{c}^{0,+}$ and $\Omega_{c}^{0}$. The ratio $\Xi_{c}^{0,+}/D^{0}$ in our
model is about 0.16 and $\Omega_{c}^{0}/D^{0}$ is about 0.012 due to the
cascade suppression of strangeness. In addition, the predicted
$\Xi_{c}^{0,+}/D^{0}$ and $\Omega_{c}^{0}/D^{0}$ ratios exhibit the
non-monotonic dependence on $p_{T}$ in the low $p_{T}$ range.
