To determine how many different 9-member teams can be chosen from 12 students, we can use the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ). Here, ( n = 12 ) and ( k = 9 ). This can also be expressed as ( C(12, 9) = C(12, 3) ), which simplifies the calculation. Thus, ( C(12, 3) = \frac{12!}{3! \cdot 9!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220 ). Therefore, there are 220 different 9-member teams that can be formed.
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