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.