Problem 1)

We have 20 kinds of presents; and we have a large supply of each kind.

We want to give presents to 12 children.

It is not required that every child gets something; but no child can get 2 copies of the same present.

In how many ways can we give presents?

Problem 2)

List all subsets of {a,b,c,d,e} containing {a.e} but not containing c

Please for problem 2, dont just give me the answer, I can find it. What I cannot find though is a general answer. Here it seems more complicated.
for {a.e} it doesn't seem to be just "from 5 objects choose 2" because we don't choose 2 random objects, but two particular objects.