What are the dimensions of the tank? If it's a standard, 24" long 15g then I would say that tiger barbs would be alright in it, but a 20" long 15H is getting pretty small for fish that like a lot of swimming room.
Now, I've personally never kept tiger barbs with cories, but rumor has it that tigers absolutely love nipping the dorsal fins of cory cats. You might want to wait for the input of someone who has actually done this before you take my word on it, though. If you do decide to stick with the barbs and cories combo, you'll want at least six barbs and at least four cories, although six would be better. For a small tank like yours, you'd probably want to introduce them in small batches to avoid overloading your beneficial bacteria.