Ginger I expect you have answered some other version of this question. It is not clearly written.
But even though that is true I admit to haveing read the quesion incorrectly.
I thought the question said 2 fruit baskets. Since the question does not appeared to have been edited i must conclude that I read it wrongly in the first place.
My original answer assumed that there are only 2 fruit baskets.
Now I will interpret it as not mattering how many fruit baskets there are, i am just fining how many individual combinations of fruite it is possible for any one fruit basket to have.
I have five apples and ten oranges. If a fruit basket must contain at least one piece of fruit, how many kinds of fruit baskets can I make? (The apples are identical and the oranges are identical.)
What can I have in a individual fruit basket..
0 apples and 1-10 oranges that is 10 posibilities
1 apple and 0-10 oranges that is 11 possibilities
2 apple and 0-10 oranges that is 11 possibilities
3 apple and 0-10 oranges that is 11 possibilities
4 apple and 0-10 oranges that is 11 possibilities
5 apple and 0-10 oranges that is 11 possibilities
Total number of what I can put in a basket is 65 possibilities.
It is a little higher than I got last time becasuse I have not considered what may or may not be in any other basket. There may not be any other fruit basket.
+118612 
