A High Definition Television Manufacturer in Asia Wants to Develop

A high definition television manufacturer in Asia wants to develop a new smart television as fast as possible using Program Evaluation and Review Technique (PERT) and must complete the design and testing work first. The objective is to be the first to market the most innovative smart television on the planet and capture the first adopter market share. The manufacturer has determined the following activities, precedence relationships, and time estimates in days for the project:
$\begin{array}{rcccr}& \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \\\text { Activity } & \text { Predecessors } & t_{o} & t_{m} & t_{p}\\\hlinea & \text { none } & 4 & 6 & 7 \\\mathrm{~b} & \mathrm{a} & 1 & 2 & 3 \\\mathrm{c} & \mathrm{a} & 5 & 5 & 5 \\\mathrm{~d} & \mathrm{~b} & 7 & 9 & 12 \\\mathrm{e} & \mathrm{b} & 2 & 4 & 8 \\\mathrm{f} & \mathrm{c} d & 6 & 9 & 10\end{array}$ Solutions are at the end of questions
-There are _____ possible paths in this project network.

A) one
B) two
C) three
D) four