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http://en.wikipedia.org/wiki/Poker_probability

I have looked over the poker probability wiki page, but I cannot figure out this homework problem:

"What is the probability that the hand dealt contains exactly two suits?"

I can justify several different approaches ... but that just means I'm wrong.

1)

(4 C 2) * ( (26 C 5) - 2*(13 C 5) )

ie choose two suits, then from those 26 cards choose 5. Now subtract the two flush hands.

2)

(4 C 2)(26 C 5) - (4 C 1)(13 C 5)

ie get the number of hands with at most two suits then subtract the number of flush hands. (4 C 1)(13 C 5) is the number of flush hands in poker.

3)

(4 C 2)(26 C 5)

JMM