Question 1067721
Since no one else is answering, I will give this one a try.
I you think my reasoning is faulty, and/or my answer is wrong, let me know.
 
Let {{{x}}} , {{{y}}} , and {{{z}}} be non-negative integers,
representing the numbers of each type of cookie in a 6-cookie assortment.
with {{{x>=y>=z}}} and of course {{{x+y+z=6}}} .
The possible (x,y,z) triples are
(6,0,0) ,
(5,1,0) ,
(4,2,0) ,
(4,1,1) ,
(3,3,0) ,
(3,2,1) , and
(2,2,2) .
Of course, there is only {{{1}}} possibility for a (2,2,2) assortment,
but other triples represent more than one assortment.
Triples with two different numbers, like (6,0,0), (4,1,1) , and (3,3,0) have {{{red(3)}}}  possibilities,
because we have {{{red(3)}}} choices for the type of cookie associated with the unrepeated number.
A triple with 3 different numbers, like (5,1,0) , (4,2,0) , and (3,2,1) represents {{{6}}} different possible assortments,
because there are {{{6}}} possible permutation of flavors triples.
So, the total number of assortments is
{{{1+3*red(3)+3*6=highlight(28)}}} .