# Topological Ordering

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.