Observations of the Cabibbo-Suppressed decays ${\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^0$, $n{\pi }^{+}{\pi }^{-}{\pi }^{+}$ and the Cabibbo-Favored decay ${\mathrm{\Lambda }}_c^{+}\to n{K}^{-}{\pi }^{+}{\pi }^{+}$

Using electron-positron annihilation data samples corresponding to an integrated luminosity of 4.5 ${\mathrm{f}\mathrm{b}}^{-1}$, collected by the BESIII detector in the energy region between $4600$ MeV and $4699$ MeV, we report the first observations of the Cabibbo-suppressed decays ${\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^0$, ${\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^{-}{\pi }^{+}$, and the Cabibbo-favored decay ${\mathrm{\Lambda }}_c^{+}\to n{K}^{-}{\pi }^{+}{\pi }^{+}$ with statistical significances of $7.9\sigma$, $7.8\sigma$, and $>10\sigma$, respectively. The branching fractions of these decays are measured to be $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^0)=(0.64\pm 0.09\pm 0.02)\mathrm{\%}$, $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^{-}{\pi }^{+})=(0.45\pm 0.07\pm 0.03)\mathrm{\%}$, and $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to n{K}^{-}{\pi }^{+}{\pi }^{+})=(1.90\pm 0.08\pm 0.09)\mathrm{\%}$, where the first uncertainties are statistical and the second are systematic. We find that the branching fraction of the decay ${\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\pi }^0$ is about one order of magnitude higher than that of ${\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}$.