The first one is correct AND this a hypergeo as long as we are selecting without relacement.
As for the second question, think of it as 3 groups.
(Just brains, no sites.)
You are selecting at least 2 from A, 3 from B, rest from C.
To do that exactly, well thats...
Next figure out all the possibilities, 3 from A, 3 from B, 4 from C....
FIND all of these and add them together. The complement here is a pain.