Thanks Rom, I just want to see if i can do this myself :)
Pat wants to select 8 pieces of fruit to bring in the car for the people he's driving to Montana with. He randomly chooses each piece of fruit to be an orange, an apple, or a banana. What is the probability that either exactly 3 of the pieces of fruit are oranges or exactly 6 of the pieces of fruit are apples?
I am going to assume that it is ok to have exactly 3 oranges AND exactly 6 apples
.... Nope that is impossible since there are only 8 peices of fruit.
8 peices of fruit
I am going to have the apples first, then the bananas and last the oranges
I'l use stars and bars too.
8 stars 2 bars
total number of possibilities is 10C2 = 45
number of combinations if there are exactly 3 oranges OOO| 1 2 3 4 5 6 6C1= 6
number of combinations if there are exactly 6 apples 1 2 3 | a a a a a a a 3C1= 3
So I think that the answer is
P(exactly 3 oranges or exactly 6 apples) = 9/45 = 1/5
I got the same as you ROM.
That doubles the chance that it is correct 
+118609 
+118609