[AaronBrown]

The general idea is simple. You hold two cards in your hand, so there are 50 unseen cards. These can flop in:

50*49*48/(3*2*1) = 19,600

ways. To solve the kinds of problems you mention, you have to figure out how many flops will qualify.

For example, if you hold two suited cards, there are 11 matching cards unseen. There are:

11*10*9/(3*2*1) = 165

ways to flop a flush. So the probability is 165/19,600 = 0.84%.

There are:

(11 * 10)/2 * 39 = 2,145

ways to flop a flush draw. The 11*10/2 is the number of ways to get two flush cards, then you could pair them with any of the 39 cards of other suits.

Counting for the straights is a bit tougher because it depends on the gap between your cards as well as the level of the cards. It's not hard to figure how many ways to flop a straight, you just have to count the number of possible straights (if you hold AK or J7, for example, there is only one straight to flop, while if you hold JT there are four). Each straight can come in 4*4*4 = 64 different ways. Open-ended and gut-shot straight draws get a bit more complicated, but it just takes careful accounting.