For these types of questions, there is a method called stars and bars that we can use for part a.
This method is as follows:
Let's put ten indistinguishable fruits in a line(the "stars")
F F F F F F F F F F
Now, to separate this line of fruits into apples, bananas, and cranberries, we can add "bars".
F F F | F F F | F F F F
^ ^ ^
apples bananas cranberries
Since we have an unlimited number of each fruit, it is a matter of how many ways we can order 10 identical fruits and 2 identical bars.
\(salads = {12! \over 10!2!}\)
a) 66
For the second part, you can bounce off of part a. The only salads that don't have two or more fruits are "plain", they only have one type of fruit in it. There are only 3 fruits, the three cases that don't work are, 10 apples, 10 bananas and 10 cranberries. Now, all we have to do is subtract 3 from the total amount.
66-3=63
b)63
(this is my first answer, I hope I'm correct!)
