We can make $$6$$ different three$$-$$digit numbers using the digits $$a$$, $$b$$, and $$c$$ without repeating digits. What is the sum of all these three$$-$$digit numbers? (Express the answer in terms of $$a$$, $$b$$, and $$c$$.) 
Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value