Multiple selection criteria, which formula? .. and selection based on unique numbers

Newbie here, be gentle

I have a couple of formula puzzles i would really appreciate some help with:

1) If i have the following type layout

Col A Col B
YES GEM-A
YES GEM-B
NO GEM-A
YES CON

I'd like to be able to count the rows where Col A contains Yes, and Col B contains the phrase GEM (not specifically GEM-A or GEM-B) Can Countif do multiple checks, i just can't get it to work! In this example, the answer returned would be 2

2) If i have the following type layout

Col A Col B
COMP 1
COMP 1
NO 1
COMP 2
COMP 3
COMP 4
NO 4

In this example, i'd like to count the amount of COMP in Col A, for the amount of 'unique' numbers in Col B, so the answer in this case would be 4 (I have to admit i have no idea in this one at all)

All help really appreciated, thanks

Jim