mathematical probabilities

[Tuff Luck]

not looking for pot odds or any of the sort:

Does anyone know where I can find the probabilities or how to find the probabilities of getting any given hand in Texas Hold em such as a pair or two pair or just high card? I'm examining the change in probability as you go up in the poker hand order for science fair this year (yes, Im in high school) and it would be much appreciated if anyone could provide me with some solid info/sources.

BTW, there are two ways I can go about doing this, but each has its set of problems. I can do it like so:

Probability of a pair (or better) in the pocket: 52/52 x 3/51
But finding out the probability of finding out pair or better with two different hole cards is tougher: 52/52 x 48/51 x 6/50 <--- I'm not sure if this is right

I can also calculate all the possible different poker hands by computing 52 given 7. (a math computation, if you don't understand it you might as well stop here) But I know this is not right because it's the best 5 card hand but I know 7 is involved somehow because you have a choice of 7 different cards so I dont know what to do in this situation. If I could somehow find out how to do it this way, it would be much easier because I could just do the total possible hands for a pair or for a straight or for trips over the total number of possible hands in hold em. (a very large number that I cant figure out although I know I am close with the above 52 given 7)

Thanks ahead of time.