Fustrated with combinations and permutation problems!!!

netigen and dkrich have the right approaches above.

I don't like the wording of the second question:

"2.) A second grade class is writing reports on birds. The students' teacher has given them a list of four birds they can choose to write about. If Lizzy wants to write a report that includes two or three of the birds, how many different reports can she write? "

No doubt she could write thousands of different reports. The question really is "how many different sets of birds could she choose to write about?"

I like what dkrich says above about seeing 'or' in the question: it's a clue that you'll need to add. The one thing to be sure of is that there's no possible overlap, as we sometimes find in Venn diagram questions. If, at a certain school, 20 people take math, and 30 people take chemistry, that doesn't mean 50 people take math or chemistry, because some might do both- the sets might overlap. Of course, there's no overlap in the birds question above: she can't write about exactly two birds and exactly three birds in the same report. So we can count each case separately and add, to get 10 as was done above.