A little while ago I made a post on here and this is basically a follow up to it as I ran into some problems.
Basically two people , player A and B, are playing a version of poker where there's 3 shared cards and they draw 2 cards each. My first problem was about calculating how many possible hands player B could win with. The answer for that is 27. Assume a third player C joins in. The problem I've gotten wrong is how many different pairs of cards can player B and C have so that both have a better hand than player A. My first thought was that because there are 27 winning hands, the max amount would be ${27 \choose 2} = 351$ without the restriction that they can't have the same card. My answer ended up being around 200, but apparently my first assumption is completely wrong as the real answer is 822.
All I want help with is understanding why my initial assumption of ${27 \choose 2}$ for the maximum amount is wrong. More context on the winning hands etc can be found here: Poker - Combination Questions
Thanks!