Can someone help me on this question:
The vertices of a triangular prism are labeled 1 through 6 such that the vertices labeled 1 and
6 share an edge and are on di↵erent triangular faces. The labels of the other four vertices are
randomly chosen with each arrangement of labels equally likely. Zhuo the ant is currently at
vertex 1. At each step of a process, he chooses a vertex adjacent to the vertex he currently
is at (i.e., connected by one edge) with a label strictly greater than the label of his current
vertex, and moves to that vertex. If there are multiple possible vertices, he chooses one
uniformly at random. For example, if he is at the vertex labeled 6, he cannot move anywhere.
What is the probability that Zhuo will eventually reach the vertex labeled 6?
And can someone help me on this unanswered one too: