To Mock A Mockingbird: Flower Garden (Math Puzzle) Question:

In a certain flower garden, each flower was either red, yellow, or
  blue, and all three colours were represented. A statistician once
  visited the garden and made the observation that whatever three
  flowers you picked, at least one of them was bound to be red. A second
  statistician visited the garden and made the observation that whatever
  three flowers you picked, at least one was bound to be yellow. Two
  logic students heard about this and got into an argument. The first
  student said: "It therefore follows that whatever three flowers you
  pick, at least one is bound to be blue, doesn't it?" The second
  student said: "Of course not!"
Which student was right, and why?

A few sample Questions from To Mock a Mocking Bird can be found here.
Answer:

The first student was right, and here is why.

Problem
I have to disagree with the authors answer. You can satisfy both the first and second statistician with combinations of two yellow and one red (YYR) or two red and one yellow (RRY)
To generate all 27 possibilities I wrote a quick Haskell list comprehension:
--ghci version 
--let r = 'R'; y = 'Y'; b = 'B'; fl = r:y:b:[] in putStr $ unlines [z|z<-[i:j:k:[]|i<-fl,j<-fl,k<-fl]]

    let r = 'R'
        y = 'Y'
        b = 'B'
        fl = r:y:b:[] 
    in  putStr $ unlines [i:j:k:[]|i<-fl,j<-fl,k<-fl]

The list of all 27 possibilities is:

RRR
RRY
RRB
RYR
RYY
RYB
RBR
RBY
RBB
YRR
YRY
YRB
YYR
YYY
YYB
YBR
YBY
YBB
BRR
BRY
BRB
BYR
BYY
BYB
BBR
BBY
BBB

But if I filter where at least one flower is yellow and least one flower is red I get:
--ghci version
--let r = 'R'; y = 'Y'; b = 'B'; fl = r:y:b:[] in  putStr $ unlines [i:j:k:[]|i<-fl,j<-fl,k<-fl,i==r||j==r||k==r,i==y||j==y||k==y]

    let r = 'R'
        y = 'Y'
        b = 'B'
        fl = r:y:b:[]
    in  putStr $ unlines [i:j:k:[]|i<-fl,j<-fl,k<-fl,
                               i==r||j==r||k==r,
                               i==y||j==y||k==y]

This list of 12 possibilities including at least one red and yellow are:

RRY
RYR
RYY
RYB
RBY
YRR
YRY
YRB
YYR
YBR
BRY
BYR

What am I misunderstanding?
 A: I think you're simply missing the part where it says "all three colours were represented" — i.e., there is at least one red flower, one blue flower, and one yellow flower in the garden.  If the garden consisted of two reds and one yellow (or vice versa), it would satisfy both statisticians' statements but not the original description of the garden.
A: I confess that I don't understand what it is you are doing with your list of all possible choices or the filter.
But: While a garden with three flowers, two red and one yellow, would satisfy the first two statistician's observations, it would not satisfy the original conditions of the problem, which requires that the garden contain at least one flower of every color (as it contains no blue flowers). Similarly with a garden with three flowers, two yellow and one red.
We know the garden contains at least one red flower, at least one yellow flower, and at least one blue flower.
The first statistician's observation amounts to saying that the garden cannot contain three or more non-red flowers: because if there were at least three flowers that are not red in the garden, then you could pick those three, and not get any red flowers. But you know there are at least two non-red flowers: at least one yellow, and at least one blue; so there cannot be more than one yellow flower, nor more than one blue flower. That means that you must have exactly one yellow flower, exactly one blue flower, and an indeterminate number of red flowers in the garden. 
The second statistician's observation, symmetrically, amounts to saying that the garden cannot contain three or more non-yellow flowers. Buy the same argument, that means that the garden contains exactly one red flower, exactly one blue flower, and an indeterminate number of yellow flowers.
Putting the two observations together tells you that the garden contains exactly three flowers, one of each color. So the first student is correct: picking "any" three flowers (i.e., picking all of the flowers in the garden) guarantees that at least one of the picked flowers is blue.

The list of "all possibilities" are just all possible ways to pick 3 flowers, assuming that there are at least three of each color. This doesn't really tell you much. Likewise, your second list seems to be all possible ways in which you can pick three flowers, with at least one yellow and at least one red, assuming that there are "enough" flowers of each color (where "enough" means here 'at least two of each color'). But in the "actual garden" not all these possibilities need be possible; indeed, a garden with exactly one blue, exactly one red, and exactly one yellow flower only allows for one possible way to pick three flowers, RYB, and the other "abstract possibilities" are irrelevant.
A: I believe either one could be correct. But, what I am wondering is this questions never explains how many of each flower was represented, just that all $3$ colors (red, blue, and yellow) are represented. Since all three flowers where represented there are $(3^3)=27$ possible that is if order matters. If order doesn't matter the possibilities are much smaller $(3*3)=9$. By what we are given by it seems like order doesn't matter. Meaning 19/27 would represent the if at least one is red or one is yellow. Which means there is only 3 combinations where red yellow and blue are selected. Without knowing how many of each are represented, logically its a safe bet to say that it is not probable that blue would have to be represented.
