Combinatorics - What is the number of ways to color n objects with 3 colors if every color must be used at least once?

problem1)
What is the number of ways to color n objects with 3 colors if every color must be used at least once?

problem2)
prove that for any three sets A,B,C ;
((AB) U (BA))^ C = ((A^C) U (B^C))  (A^B^C)      ^ means intersection
                                                  
Please explain the steps, help me understand.
Thanks