Median poker hand (Texas Hold’em)

Question

I try to find the median poker hand (Texas Hold’em). The following is given:

1) There are 52 cards

2) Assuming seven of them are chosen randomly

3) Create the best possibility with 5 of these 7 cards (see this list)

Probably it could be done by by just generating all $nCr(52,7)$ card combinations, get always the best poker hand and order all these results. Unfortunately this does not seem to be very easy.

Maybe there is a math trick to simplify this or someone just know the answer (e.g. 5♥ 5♣ 4♦ 3♠ 3♣)?

Thank you very much

Answer 1

From this list for best 5 from 7 one pair starts at 38.8% and ends at 82.6%.
So using liner interpolation QQ is the median hand.