A few poker math questions

[BBD]

Hello. I am a read these forums regularly and post once in a while, however I have just starting reading probability threads in the last few days. I had a few questions on the math.
A freind of mine just finished reading HPFAP for the first time yesterday. The authors state in Appendix A: Probability that 2 suited cards will make a flush 6.5 percent of the time, assuming one will stay for all five community cards. My friend asked me to show him this on paper, and to be honest about it, I wasn't able to do it. I undertsand my 'outs' and the like, I've just never been shown the proper way to work this out on paper. Any help is greatly appreciated.

Thanks!

ps- what are the odds of connecters making a staight? how about one gappers? thanks again!

[yellowjack]

You start with 2 suited cards, so that leaves 11 cards of your suit and 39 offsuit cards out of the remaining 50 cards in the deck.

C(50,5) is total number of different community card combinations.
The board of Jh Qh Kh Ah Ac
is different from Jh Qh Kh Ah As

P(3 of your suit) = [ C(11,3)*C(39,2) ] / C(50,5) = 0.0577
P(4 of your suit) = [ C(11,4)*C(39,1) ] / C(50,5) = 0.0060
P(5 of your suit) = [ C(11,5)*C(39,0) ] / C(50,5) = 0.0002

Add up the 3 probabilities and you get 0.0639, which is 6.4% when rounded up.

[BBD]

thank you kindly yellowjack