Let's suppose you can use a character set of, say, 40 symbols of unambiguous upper,lower and numeric characters.
For a sequence of n chars, you've got 40^n40n combinations
- 40^4404 = 2,560,000
- 40^5405 = 102,400,000
- 40^6406 = 4,096,000,000
- 40^7407 = 163,840,000,000
- 40^8408 = 6,553,600,000,000
Thus 8 chars gives a pretty good space to work in - if you generated 10 million codes, you'd have to try hundreds of thousands of combinations to brute force a code.
Or you come at from the other direction - give the number of possible codes, how many codes should you generate to avoid the trap they call the Birthday Paradox?
Taking the 8 char code, 6,553,600,000,000 is approx 2^42242, thus you might reasonably generate 2^21221 codes from it, or 2,097,152