3 card probability question

[jjp]

At a home game, we play a version of "guts" where three cards are dealt, and you make a two card "high" hand. How can I calculate what the odds are of having various hands such as (and the odds of anyone at the 6 handed table having):
66 or better
Any pair
AJ or better

We then deal two more cards (total of 5) where we play a 3 card low (straights and flushes ignored). What are the odds of a:
Rough 5 or better
Rough 6 or better
Rough 7 or better?

Thanks.