To do these you need to know basic set theory.
Prove:
P{(AuB)nC} = P{AnC} + P{BnC} - P{AnBnC}
u denotes union
n denotes intersection
Here is what I have so far. (To prove I'm not just posting questions without trying.) I'm probably in the completely wrong direction.
P{(AuB)nC} = P(A) + P(B) + P(C) - P(AuBuC)
P{(AuB)nC} = P(AuB) + P(AnB) + P(C) - P(AuBuC)
P{(AuC)n(BuC)} = P(AuB) + P(AnB) + P(C) - P(AuBuC)
P(AuB) + P(AnB) + P(C) = -p(AuBuC) - P{(AuC)n(BuC)}
If that is true then there is absolutely no reason for you to have been placed in a course that requires these proofs. You need to make your academic advisor aware of this situation. If you are in a course that does require these proofs, then you should consider taking first a course in foundations(set theory). That is where you will find these ideas.