As we might see a paired flop about 17% of time, let's take a look at what kind of hands players might have.
Possible starting hands: 1176=49*48/2=C(49,2) we can see here the possible starting hands are updated based on the flop (based on the fact).
Four of a Kind: 1
Three of a Kind or Full House: 2*47 + 3 = 97 type 1: pick one card with the same number as the paired card(2) and pick anyone from the remaining card without the same number(47), type 2: pick two cards from with the same number as the unpaired card(3)
Two Pair: 198=3*44+11*6 type 1: pick one with the same number as the unpaired card(3) and pick anyone from the remaining card without the number in the flop(44), type 2: pick any paired card without the number in the flop (11*6)
Others: 880=44*40/2=C(11,2)*4^2 pick any unpaired card without the number in the flop
There is about 25% (1 in 4) having a two pair or better.
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The previous 3 cards or 5 cards analysis give players an idea of what might happen during the game before you see the flop or give a general idea of the distribution of the combinations.
But after you see the flop, the situation is changed. You will have to update the distribution of the combinations based on the flop or based on the fact.
By the way, you also have two cards at hand, so what the other players might have will be different from the previous calculated numbers.
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