mathematical probabilities

[lightfungus]

to defend my previous quote against all you mean people.
I can tell you the probability of any 5 card hand using the (n choose k) notation. This notation is used to represent the following formula:

n!/(k!(n - k)!)

For example, to find the probability of, say, a pair we have:

((13 choose 1)*(4 choose 2)*(12 choose 3)*(4 choose 1)^3)/(52 choose 5)
A B C D E

A: first we have to choose one of the 13 ranks of cards for our pair.
B: next, out of that rank we just chose, we choose 2 of them. AFter all, out of those four cards there are 6 possibilites and we have to consider that.
C: We must now exclude the rank that we already chose, and choose three different ranks out of the remaining 12 in order to avoid 2 pair.
D: then we have to choose one suit out of those 3 ranks.
E: Finally, all that has to be over the possibility of every 5 card hand.

And we get:
(13*6*220*64)/(52 choose 5 [a really big number like 2599388ish]) =0.422569 or 42.2%

So as i was saying in my previous quote...wait no i was wrong.
BUT, to find the probability of a finished hand( i.e. after the river) you multiply the probability of the 5 card board times the probabilty of your hole cards (52 choose 2) and that should be your answer.

THank you Georgia Tech Probabilty with Applications. Any questions?