duplicate numbers in ball drawing experiment

The answer in both cases is 1 - P(no balls match).

3 buckets:
The probability that the second ball doesn't match the first is 9/10. The probability that the third ball doesn't match the first two is 8/10. 1 - (9/10 * 8/10) = .28

4 buckets:
The probability that the second ball doesn't match the first is 9/10. The probability that the third ball doesn't match the first two is 8/10. The probability that the fourth ball doesn't match the first three is 7/10. 1 - (9/10 * 8/10 * 7/10) = .496

Thank you so much!