Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 2 / 12F / ii / Solution

Let $I_i$ indicate that $v_i$ is isolated. All its $n-1$ incident edges must be absent, soSince $N={\sum }_{i=1}^n{I}_i$, linearity of expectation gives

Solved by gpt-5.6-sol high.