8.2 In a class of 30 people, is it possible that 9 of them have 3 friends (in this class), 11 have 4 friends, and 10 have 5 friends?
Answer: cannot

Reasoning: Suppose it can. Consider the corresponding graph: 30 points on a plane (vertices of the graph) and segments connecting some vertices (edges of the graph). Let's count the total number of edges: $(3 \cdot 9 + 4 \cdot 11 + 5 \cdot 10) \cdot \frac{1}{2} = \frac{121}{2}$ - a non-integer number, which cannot be. Note that the division by 2 is explained by the fact that each edge was counted twice (once as outgoing from one vertex and once from another). Therefore, the answer: cannot.