Problem $2(8$ points$)($CLO$1,3,4)$: Circle the best answer among the given choices:

$($Answer the following two questions based on this problem:$)$

For the map shown below, assume that we want to color it with three colors $($Red$,$ Green, and Blue$)$ given that no two adjacent areas get the same color. The enhanced backtracking algorithm is to be used in the assignment process.

Assume that we have already colored A with Red and E with Green. Now, which area should be colored next and what color it should be given:

A$)$ C with blue

B$)$ D with blue

C$)B$ with green

D$)B$ with blue

How many valid solutions are there for this coloring problem:

A$)24$

B$)12$

C$)6$

D$)32$