> The obvious first step is to figure out how many possible hands there are, which is a simple enough operation. Assuming that you're playing by yourself (in which case you're being killed to death by the rake), the total number of possible spreads is (52 * 51 ... 46), or 674274182400. (Note to gremlinn: Is there a more convenient notation for (52 * 51 ... 46)? Like maybe 52!46? If there isn't, I'm going to write to the Federal Bureau of Math Notation and demand one.)

52P7, that is the number of permutations of 7 items taken in a set of 52.

And in fact the number of spreads would be this only if the order in which you draw the cards is important (i.e. drawing first the 10 of hearts then the 7 of spades is not the same as drawing first the 7 of spades then the 10 of hearts). Otherwise you are off by a factor of 7! (=5040).

You might want to take a look at "Number of permutations" (nPr = n!/(n-r)!) and "Number of combinations" (nCr = n!/(r!(n-r)!)) in some mathematical source (like http://mathforum.org/dr.math/faq/faq.comb.perm.html).

>
> Now we'll go with a pair (...)

I didn't try to follow all the math, but you might be interested by this: http://www.whichpoker.co.uk/online_poker/poker_probability.htm

My"not gremlinn"rth