% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
format rat;

P_F  = nchoosek(13,8) * nchoosek(39,18) / nchoosek(52,26)
fprintf("%10.6f\n",P_F);

P_EF = nchoosek(13,3) * nchoosek(52-13,10) * nchoosek(10,2) * nchoosek(52-13-10,11) / (nchoosek(52,13) * nchoosek(39,13))
fprintf("%10.6f\n",P_EF);

P_E_G_F = P_EF / P_F
fprintf("%10.6f\n",P_E_G_F);

% the "second" way to work this problem:
% 
% S_F  = nchoosek(13,8) * nchoosek(39,18) * nchoosek(26,13) * nchoosek(26,13);
% S_EF = nchoosek(13,8) * nchoosek(39,18) * nchoosek(26,13) * nchoosek(5,3) * nchoosek(21,10);
% S_S  = nchoosek(52,13) * nchoosek(39,13) * nchoosek(26,13);
% P_F  = S_F / S_S 
% P_EF = S_EF / S_S 

% S_EF/S_F % = 0.33913