pick three drawing

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Our veterans club has a daily pick 3. We currently have one cage with 30 balls numbered 0 thru 9. The first number is drawn and returned to the cage and the next two the same way. I believe this gives an advantage to someone with triple or double numbers (111 or 112) if 1 is the first number drawn. Wouldn't 10 balls in a single cage (number drawn returned to the cage) be the correct way to pull the pick 3? This would be similar to what the state lottery does, except they use 3 cages with numbers 0 thru 9<

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Assuming that each number 0 through 9 appears exactly 3 times, then the answer is no- both methods of drawing are equivalent.

Since the number drawn is returned to the cage after each drawing, each drawing is an independent event.

In fact, you could put as many balls into the cage as you wanted, and as long as each number was represented proportionally and the number drawn was replaced after each draw, all pick-3 combinations from 000-999 are equally as likely to be selected.