Need help with number 9-12. 9. Let n be a positive integer, and let Sn stand for the directed graph with one vertex for each integer from 0 to n

12. Recall the graph dynamics problem we did in class, in which we started with a number of vertices and added edges randomly. Suppose we start with just 5 vertices. What is the probability that the graph will be connected after 3 edges are added? If you can’t tell the probability exactly, give a reasonable guess and explanation. Repeat the problem with 4 edges, 5 edges, 10 edges, and 20 edges (if reasonable; go as far as you can reasonably go!) (Remark: to simplify the problem, let’s allow the addition of multiple edges between two given vertices if the same pair comes up more than once. This means you don’t have to worry about whether an edge is “really added” each time.)