We investigate the following quasilinear and singular problem,$$\text{t}o2.7cm\left\{\begin{array}{cc}-{\Delta}_{p}u=\frac{\lambda}{{u}^{\delta}}+{u}^{q}\phantom{\rule{1.0em}{0ex}}\hfill & \phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\Omega ;\hfill \\ {u|}_{\partial \Omega}=0,\phantom{\rule{1.0em}{0ex}}u\>0\phantom{\rule{1.0em}{0ex}}\hfill & \phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\Omega ,\hfill \end{array}\right.\text{t}o2.7cm\phantom{\rule{4.0pt}{0ex}}\text{(P)}$$where $\Omega $ is an open bounded domain with smooth boundary, $1\<p\<\infty $, $p-1\<q\le {p}^{*}-1$, $\lambda \>0$, and $0\<\delta \<1$. As usual, ${p}^{*}=\frac{Np}{N-p}$ if $1\<p\<N$, ${p}^{*}\in (p,\infty )$ is arbitrarily large if $p=N$, and ${p}^{*}=\infty $ if $p\>N$. We employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in ${W}_{0}^{1,p}\left(\Omega \right)$. While following an approach due to Ambrosetti-Brezis-Cerami, we need to prove two new results of separate interest: a strong comparison principle and a regularity result for solutions...