(i) If both boys are in the team, we need to choose 2 more people from the remaining 7 people (3 girls and 4 adults). The number of ways to choose 2 people from 7 is given by the combination formula: \(\binom{7}{2} = 21\).

(ii) If the adults are either all in the team or all not in the team, we consider two cases:

• All adults in the team: This is not possible since the team size is 4 and there are 4 adults.
• All adults not in the team: We choose all 4 members from the 5 non-adults (2 boys and 3 girls). The number of ways is \(\binom{5}{4} = 5\).

Thus, the total number of ways is \(1 + 5 = 6\).

(iii) If at least 2 girls are in the team, we consider two cases:

• 2 girls in the team: Choose 2 girls from 3 and 2 others from the remaining 6 people (2 boys and 4 adults). The number of ways is \(\binom{3}{2} \times \binom{6}{2} = 3 \times 15 = 45\).
• 3 girls in the team: Choose 3 girls from 3 and 1 other from the remaining 6 people. The number of ways is \(\binom{3}{3} \times \binom{6}{1} = 1 \times 6 = 6\).

Thus, the total number of ways is \(45 + 6 = 51\).