# Texas hold 'em, flush probability

Suppose you are playing Texas Hold'em poker and you are dealt the ace of hearts and the ten of hearts. What is the probability that you make a flush with exactly three more hearts on the board by the river?

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You have seen the ace and ten of hearts so there are 11 other hearts and 39 non-hearts among the 50 unseen ...

#### Solution Summary

When starting with two suited cards, this solution finds the probability a poker player makes a flush with exactly 3 cards of the same suit on the board.

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