Expected number of vertices with degree 2 A simple graph with $n$ vertices is constructed by randomly and independently placing an edge between every two vertices with probability $p$. What is the expected number of nodes with degree two?



I was only able to find the probability of any vertex having degree 2. Let me explain what I tried. For any vertex we can have n-1 edges connecting it(since its a simple graph), so for it to have degree = 2, two of these n-1 edges should be there, and rest not. 

This gives: $\binom{n−2}{2}p^2(1−p)^{n−3}$.
Hint:


   Indicator random variables.


If that's not enough and you need a second hint:


   Use linearity of expectation.