Among $E, B \text{and }C$, you can choose exactly two edges, because choosing less than 2 edges will make the tree disconnected and choosing 3 edges will add a cycle to the tree. Hence, there are $^3C_2 = 3 $ ways. Similarly, there are $3$ ways to choose edges from $A, D \text{and } E$. So, total possible ways = $3*3=9$.
