Binomial[10,1]

num=1000;

a = Table[{i,Binomial[num,i]},{i,0,num}];
ListPlot[a,Filling->Axis,PlotRange->All,LabelStyle->Directive[Black,FontFamily->"Helvetica"]]

a = Table[{i,Log[Binomial[num,i]]},{i,0,num}];
ListPlot[a,Filling->Axis,PlotRange->All,LabelStyle->Directive[Black,FontFamily->"Arial"]]

prob = ((Binomial[num,0])/((∑_(i=0)^num)Binomial[num,i]))//N