function [] = chap_3_prob_41()
% 
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

format rat 

% compute the individual probabilties: 
for k=3:-1:1, 
    nchoosek( 3,k )*nchoosek( 52-4, 26-k ) / nchoosek( 51, 26 ) 
end

% perform the required summation: 
s=0.;
for k=1:3
    s = s + (k/26)*(nchoosek( 3,k )*nchoosek( 52-4, 26-k ) / nchoosek( 51, 26 ));
end
s

(1/27) + (26/27) * (1/17)