Couple of Stud 8 questions

[djk123]

I would like to know the answers to these questions, but I'd also like to know how to get the solutions if anyone could explain. Any help is greatly appreciated.

Assume heads up stud 8 game. Whenever I say a low card, I mean a card between Ace and 8.

Given you are dealt 3 unique cards 8 or lower, with no cards of the same suit, what is the probability that you receive either a pair or a 4th low card if
(a) opponent has low doorcard
(b) opponent has 9-K doorcard


Given you are dealt 3 unique cards 8 or lower, with 2 cards of the same suit, what is the probability that you receive either a pair, a 4th low card, or a card giving you a 3 flush if
(a) opponent has low doorcard
(b) opponent has 9-K doorcard

Given your opponent has a low doorcard, what is the probability that he has either 3 unique low cards, a pair, 3 cards of the same suit, or rolled trips if
(a) you hold Ace low big
(b) you hold 3 big cards