How many possible different lists out of given subjects

Question

It's a college task. I Know how to find permutation of numbers, letters etc., but this is completely different. Here's the task :

 

A Student is studying in a university. All study modules (subjects) are selective. All need to be picked. Some modules can be selected only after certain modules are picked. The student need to form a study program, in which the modules would form a list. Modules that make up the list depend on the earlier picked modules. How many different lists can there be ? 

Data is arranged like so : Module code, Module name, Number of modules that the given depends on, dependent modules codes;

IF01 Programming 0
IF02 Maths 1 IF01
IF03 Data structures 2 IF01 IF02
IF04 Digital logic 0
IF05 Mathematical logistics 1 IF04
IF06 Operations optimization 1 IF05
IF07 Algorithm analysis 2 IF03 IF06
IF08 Programming theory 1 IF03
IF09 Operating systems 2 IF07 IF08

Help Please. 

Answer 1

Draw a PERT Chart showing possible sequences.

Modules IF01 and IF04 have 0 prerequisites. Each of them may be the starting point of a list, so there are already 2 possibilities for the first element of the lists.

Consider for a moment linkages A-B and X-Y. How many possible lists?
A,B,X,Y
A,X,B,Y
A,X,Y,B

X,Y,A,B
X,A,Y,B
X,A,B,Y

Either A or X must start the list, The linkages must stay in prerequisite order. What is the formula so fat?

Then consider linkages A-B-C and X-Y. How many possible lists?

So, determine the linkages, then the number of possible lists.

Note: the modules are nicely numbered and the counts of prerequisites are given, so that the completeness of the diagram may be easily checked.