$3.$ Consider the following graph with edge weights listed in the table.

$($a$)$ What is the cost of its minimum spanning tree?

$($b$)$ How many minimum spanning trees does it have?

$($c$)$ Suppose Kruskal's algorithm is run on this graph. In what order are the edges added to the MST $($in case of ties add the edge which is lexicographically first, that is$,$ comes first in the table$)?$ For each edge in this sequence, give a cut that justifies its addition.