Here is some of what I figure out but I'm still stuck here.. I Label The card with its number and color (e.g. Heart Ace is written as 1H, Spade King is 13S, Diamond 10 is 10D, Club 4 is 4C), then each outcome is a pair of two distinct cards (e.g. (1H,2S), (3S,2C), etc.).
We can write down a few examples from this sample space:
(1H,2H),(1H,3H),....,(2H,3H),(2H,4H),...,...
(1H,2S),(1H,3S),....