5. Consider the following graph:
[25 pts]
1
c
2
b
a
d
0
3
e
Assuming the weights are all different there are 5! = 120 possible orderings, for example
$a < b < c < d < e$ and $e < d < c < b < a$ and $a < c < b < e < d$ and so on. Assuming each
of these is equally likely, if we run Kruskal's Algorithm on this graph, what is the probability
that $a$ is chosen?
Note: Do not do this by listing all possible orderings and explain your work with sentences,
not just calculations!
Solution:
