Question $1$

All parts of this question concern the following DAG.

What is the number of different topological orderings of the DAG?

List the topological ordering of the DAG obtained by the algorithm that repeatedly outputs the next vertex of in$-$degree $0$ and

removes the vertex and its edges. Assume that ties, if any, are broken in alphabetical order. Each entry below must be from

$\{a,b,c,d,e,f,g,h\}.$ Provide the number of different topologicatopological orderings of the DAG as well.