Poker

Here is a link that explains everything.

http://en.wikipedia.org/wiki/Poker_proba...oker_hands

For the question involving pairs, the answer is 4C2*13*12C3*4^3 = 1,098,240

4C2 tells number of combinations of pairs of a certain rank.
13 is the number of ranks.
12C3 is the number of combinations of ranks that don't share the rank of the pair.
4^3 relates to the number of suits per card (the cards that aren't in pairs).

Alternative (better) explanation for poker pairs problem:

http://mathforum.org/library/drmath/view/56500.html