We need to consider two cases: when Tom and Henry are both in the team and when both are not in the team.

Case 1: Tom and Henry are both in the team.

If Tom and Henry are in the team, we need to choose 1 more boy from the remaining 10 boys. This can be done in \(\binom{10}{1}\) ways. We also need to choose 3 girls from 9, which can be done in \(\binom{9}{3}\) ways.

The number of ways for this case is:

\(\binom{10}{1} \times \binom{9}{3} = 10 \times 84 = 840 \text{ ways}\)

Case 2: Tom and Henry are both not in the team.

If Tom and Henry are not in the team, we need to choose 3 boys from the remaining 10 boys. This can be done in \(\binom{10}{3}\) ways. We also need to choose 3 girls from 9, which can be done in \(\binom{9}{3}\) ways.

The number of ways for this case is:

\(\binom{10}{3} \times \binom{9}{3} = 120 \times 84 = 10080 \text{ ways}\)

Total number of ways:

Adding both cases together, we get:

\(840 + 10080 = 10920 \text{ ways}\)