The total number of 4-person subcommittees that can be formed from a 30-member club is:
C(30,4) = 27,405
To find the number of 4-person subcommittees that have at least 3 juniors, we can use the complement rule and subtract the number of subcommittees with 0, 1, or 2 juniors from the total number of subcommittees.
Number of subcommittees with 0 juniors:
C(12,0) * C(18,4) = 3060
Number of subcommittees with 1 junior:
C(12,1) * C(18,3) = 13,860
Number of subcommittees with 2 juniors:
C(12,2) * C(18,2) = 16,830
Total number of subcommittees with 0, 1, or 2 juniors:
3060 + 13,860 + 16,830 = 33,750
Therefore, the number of 4-person subcommittees that have at least 3 juniors is:
27,405 - 33,750 = -6,345
This result is not possible, as the number of subcommittees with at least 3 juniors cannot be negative. This could be due to an error in the calculation or an incorrect assumption.