Re: how many possible combinations? Start with the pocket pair:
2 cards from 4 gives you 6 possible PP for each 'rank'
5 ranks 10-10 to A-A gives 6*5 = 30 possible pocket pairs
Theres 52*51/2 = 1326 possible hole hands so probability of premium pocket pair is 30/1326 = 0.0226(2.26%)
Assuming you have a pocket pair there are now only 50 cards in the deck
For 2 High cards:
First Assuming you have AA
for the AK, AQ, AJ, A10 you have a 2/50 chance of getting your A then a 16/49 chance of your other card
(2/50)*(16/49)=0.013
for the KQ it's 4/50*4/49 = 0.065
Second assuming you have KK-1010
Chance of A = 4/50
chance of other card = 14/49
probability = 0.023
for KQ it's
4/50*4/49 = 0.065
or
2/50*4/49 = 0.003
or
4/50*2/49 = 0.003
SO:
Chances of you holding 10-10 to AA = 0.0226
chances of your opponent holding the hands you mentioned in this case = (I think the sum of all the probabilities mentioned above, although I think I might be wrong on that) = 0.094
Chances of both = 0.0226*0.094 = 0.0022 = about 0.2%
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