PERT Chart exercise - is there enough information to solve?

Question

I'm posting this here as my question is from a computer science textbook. It is not a homework question as I am self-studying and I have the answers available.

In the exercise below, I can't see how I'm supposed to know which activity to place on which arrow. I can't tell if there is insufficient information provided or if it is a lack of understanding on my part which makes it impossible to decide which arrow out of node 2 should have be labelled B and which with C for example.

If it is solvable given the information provided, could someone please exaplain the method?