Given that the three positive integers $$a$$, $$b$$, and $$c$$ are such that $$a+b+c=31$$, find the largest value of $$abc$$. 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums