Right you are,
Legate - that's what I thought, too. I'm sorry, I just forgot to tell the number of people. That happens when you're up when you should be sleeping, after a horrible exam week.
As for whether Frodo and Balin ever met, I don't think so. Frodo was, after all, only twenty-one when Bilbo adpted him, and Balin entered Moria the same year.