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The multihadron decays $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ and$\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ are observed in data correspondingto an integrated luminosity of 3fb$^{-1}$, collected in proton-protoncollisions at centre-of-mass energies of 7 and 8TeV by the LHCb detector. Usingthe~decay $\Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^-$ as anormalisation 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 isstatistical and the second systematic. The ratio of branching fractions for$\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^+ p\pi^-\pi^-$ decays is found to be $$ \frac{ {\mathcal{B}} (\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^- )}  { {\mathcal{B}} ( \Lambda_b^0\rightarrow D^{+} p \pi^-\pi^- )}  \times  (  {\mathcal{B}}( D^{*+} \rightarrow \pi^0 ) +  {\mathcal{B}}( D^{*+} \rightarrow \gamma ))  = ( 61.3 \pm 4.3 \pm 4.0 ) \% \,. $$

Observation of $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ decays