2.17. For a given code c:ST, let C(x,y) be the two-variable generating function for the numbers qr(i) defined above, that is C(x,y)=i,rqr(i)xiyr. Prove that C(x,y)=yQ1(x)/(1yQ1(x)) 16. Let S={a,b,c,d,e,f,g} and suppose that a binary code is defined by a00,b010,c011,d1000,e1001,f1101,g1111. Write down the generating function Q1(x) and hence calculate Q2(x) and Q3(x). What do the coefficients of x7 in Q2(x) and Q3(x) represent? Verify your answers by making lists of the corresponding elements of S