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)}