III.A.1.  How many different five-scoop dishes are possible when all scoops have to be different flavors? 

>	binomial(26,5);

 

III.B.1.  How many different five-scoop dishes are possible if there is no prohibition against repeating flavors? 

>	binomial(5+26-1,5);

 

III.C.  How many different five-scoop dishes are possible if there can be no more than two vanilla scoops, at most one chocolate scoop, and no more than three strawberry scoops? 

>	with(powseries):

 

>	vanilla := powpoly(1+z+z^2,z):

 

>	chocolate := powpoly(1+z,z):

 

>	strawberry := powpoly(1+z+z^2+z^3, z):

 

>	other := powpoly(1+z+z^2+z^3+z^4+z^5, z):

 

>	genfct := evalpow(vanilla*chocolate*strawberry*other^23):

 

>	tpsform(genfct,z,6);

 

Answer = coefficient of z^5, i.e., 138854.