The multihadron decays $\Lambda b0\to D+p\pi -\pi -$ and $\Lambda b0\to D\ast +p\pi -\pi -$ are observed in data corresponding to an integrated luminosity of 3fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, collected in proton-proton collisions at centre-of-mass energies of 7 and 8TeV by the LHCb detector. Using the~decay $\Lambda b0\to \Lambda c+\pi +\pi -\pi -$ as a normalisation channel, the ratio of branching fractions is measured to be $$ \frac { {\mathcal{B}} ( \Lambda_b^0\rightarrow D^+ p \pi^-\pi^- ) } { {\mathcal{B}} ( \Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^- ) } \times \frac { {\mathcal{B}} ( D^+ \rightarrow K^-\pi^+\pi^+) } { {\mathcal{B}} ( \Lambda_c^+ \rightarrow p K^-\pi^+ ) } = ( 5.35 \pm 0.21 \pm 0.16 ) % ,, $$ where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for $\Lambda b0\to D\ast +p\pi -\pi -$ and $\Lambda b0\to D+p\pi -\pi -$ decays is found to be $$ \frac{ {\mathcal{B}} ( \Lambda_b^0\rightarrow D^{+} p \pi^-\pi^- )} { {\mathcal{B}} ( \Lambda_b^0\rightarrow D^{+} p \pi^-\pi^- )} \times ( {\mathcal{B}}( D^{+} \rightarrow \pi^0 ) + {\mathcal{B}}( D^{*+} \rightarrow \gamma )) = ( 61.3 \pm 4.3 \pm 4.0 ) % ,. $$