Each of the numbers above represents the number of cards of a certain suit on a five card board. There are six different ways the board can be set up taking only suits into consideration, only 2 of them cannot result in a possible flush. You will notice that in each case the numbers shown add up to 5, the 5 community cards. A completely suited board, all 5 cards of the same suit, would be represented as (0,0,0,5). It might look like this A♦J♦6♦3♦2♦. This is of course a flushing board or meadow as The Professors friend Bib Ladder calls it. The next 3 types represent only possible flush boards. (0,0,1,4) 5♠K♥Q♥10♥2♥. Notice that there are 0 clubs, 0 diamonds, 1 spade and 4 hearts. (0,1,1,3) might look like this 3♣3♥9♣J♣4♦ and(0,0,2,3) the last flushing board, could be 6♣10♦A♦K♣Q♣. In the next 2 examples no flush is possible (1,1,1,2) A♥A♣A♦A♠K♥ (I'm betting this one anyway)
and (0,1,2,2) 3♥2♦6♦4♣5♥ (I'll check here).
It's funny that you asked about this one Chuck. I just read the Flushing Meadow articles last week.