Measurement of the decays D0→π+π+π−π−, D0→K−K+ and Ds+→Φπ+π+π−

We present measurements of the branching ratios for two Cabibbo suppressed decays of the D 0 meson, D 0 →π + π + π − π − and D 0 →K − K + , and for the decay D s + →Φπ = π + π − . The physics signals were extracted from a data sample consisting of 60 million triggers, collected by Fermilab Photoproduction Experiment E687 from December 1987 to February 1988. The relative branching ratios are measured to be : Γ(D 0 →4π)/Γ(D 0 →K3π)=0.108±0.024±0.008, Γ(D 0 →Kπ)=0.138±0.027±0.010 and Γ(D s →Φ3π)/Γ(D s →Φπ)=0.58±0.20±0.10