probability of getting flush with suited hand

[BruceZ]

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Hey,

I'm just wondering, when you use C(39,2), C(39,1), etc on your three examples, what is the reasons for using those numbers?

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There are 39 non-flush cards and 11 flush cards remaining. C(39,2) is the number of combinations of 2 non-flush cards, and C(11,3) is the number of combinations of 3 flush cards, so C(11,3)*C(39,2) is the number of ways to make a flush with exactly 3 flush cards and 2 non-flush cards on the board.

C(39,1) = 39 is the number of non-flush cards, and C(11,4) is the number of combinations of 4 flush cards, so C(11,4)*C(39,1) is the number of ways to make a flush with exactly 4 flush cards and 1 non-flush card on the board.