I have learnt to solve topological ordering using $in-degree$ method where we have to take the vertices having in-degree $0$ at an instance and arrange them in that order.
For example consider this question asked in Graduate Aptitude Test in Engineering more commonly known as $GATE$ the entrance exam for $IIT$ $M.Tech$ in India. The question goes like this,
Find the number of topological ordering possible for the given graph-->
Here we can see that in-degree of A is 0 so we take $A$ as the stating vertex, then we have 2 options either $B$ or $C$, and so on.... The number of possible topological ordering in this case is $6$ as explained below
This method works well for these examples where the number of in-degree 0 vertices is less at a time, but how to solve problems where there are many number of 0 in-degree vertices as the one given below
I think combinatorics will come into picture in such cases, but I am unable to apply it properly. Any help will be highly appreciated.