What are the answers you are given? Is your answer to part (a) "correct"?
If so, then they are treating the individual coconuts as distinguishable (as you did), and pka's answer would also be correct. (The 10 comes from thinking of the coconuts as 1 group from the first tree, 4 nuts from the second, and 5 from the third, and arranging those 10 items in any order.)
I would have taken the wording of the problem as (possibly) suggesting that it is only the origin of each coconut that can be identified, so that individual coconuts are not distinguishable, so the problem would be equivalent to arranging AAABBBBCCCCC, keeping the AAA together. But it sounds like that is not what was intended.