Thank you Anthrax, I am able to understand the problem now, it took a quite a while to process. :))
Dear Melody,
I'm not sure if this is helpful, but it's always nice to think about it in small cases.
Let's say I have a pair of jokers (j, j) and a pair of ones (1, 1). I randomly mix it up and draw cards until I get a pair, by symmetry, I will draw the pair of ones first 50% of the time, and will draw the pair of jokers first 50% of the time. Notice how this is the same as the probability of having two cards (1, j), and seeing which card I draw first. I will draw the one first 50% of the time, and will draw the joker first 50% of the time.This is because since both cards are pairs(1, 1 and j, j), the probability of which pair you draw first is still the same as is if you were to draw two non-paired cards (1, j).
Hope it makes a bit more sense.
=^._.^=