Example 2.1.4 Two organizations, A and B, have a total of 11 members, with 7 from organization A and 4 from organization B. A 5-person team is to be formed from these members. (1) If the team must include 2 members from organization B; (2) If the team must include at least 2 members from organization B; (3) If a specific member from organization B and a specific member from organization A cannot be in the team at the same time, how many different ways can the team be formed in each case?
Solution: (1) There are $\mathrm{C}_{4}^{2}$ ways to choose 2 people from unit B, and $\mathrm{C}_{7}^{3}$ ways to choose 3 people from unit A, making a total of $\mathrm{C}_{4}^{2} \mathrm{C}_{7}^{3}=210$ ways.
(2) $\mathrm{C}_{4}^{2} \mathrm{C}_{7}^{3}+\mathrm{C}_{4}^{3} \mathrm{C}_{7}^{2}+\mathrm{C}_{4}^{4} \mathrm{C}_{7}^{1}=210+84+7=301$.
(3) If person $B$ from unit B cannot be with person $A$ from unit A, we only need to exclude the cases where both $A$ and $B$ are in the 5-person group. Therefore, there are $\mathrm{C}_{11}^{5}-\mathrm{C}_{9}^{3}=462-84=378$ ways.