Probability of hitting on the flop

[SittingBull]

If U have AKs,then there are 3 A's that are favorable for flopping exactly a pair of A's.
Since U have 2 cards in your hand,there are 50 cards that U do not see.
Of the 50 cards, 3 are favorable,so 47 are unfavorable.
The odds against hitting exactly a pair of A's is the ratio: unfavorable outcomes:favorable outcomes.
For floppong a flush draw. U have two suited cards. So U need two of the remaining 11 suited cards to flop a flush draw.
The total # of combinations of flopping 3 cards from 50 remaining unknowns is C(50,3).
Of these,there are C(11,2) favorabe outcomes. This is the total # of ways of hitting 2 of your suited cards grom a group of 11 of the same suit.
Hence, the probability of flopping a 4-flush is # of favorable outcomes/total # of outcomes.
Hence C(11,2)/C(50,3).

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