e1  = 0; e2 = 2; e3 = 9;

Z[t_] :=  
      Exp[-e1/t] + Exp[-e2/t]  +  Exp[-e3/t]

Plot1 = Plot[Z[t], {t, 0, 30}]

Plot2 = Plot[Exp[-e1/t]/Z[t], {t, 0, 30}]

Plot3 = Plot[Exp[-e2/t]/Z[t], {t, 0, 30}]

Plot4 = Plot[Exp[-e3/t]/Z[t], {t, 0, 30}]

Show[Plot1, Plot2, Plot3,  Plot4, 
      PlotRange -> {{0, 30}, {0, 3}}]