Suppose we apply Prim's Minimum Spanning Tree $($MST$)$ algorithm to the weighted graph $G$ shown below starting from vertex $a.$ Let $T$ denote the resulting MST$.$

Time left $3$:$17$:$14$

$($If more than one answer is correct, select the one in red.$)$

a$.$ Edge $(e,i)$ is the $8^{th}$ edge added to $T.$

b$.$ More than one of the other choices are correct.

c$.$ There are at most $5$ edges on the unique simple path in $T$ between vertices $b$ and $j.$

d$.$ Edge $(b,c)$ is the $9^{th}$ edge added to $T.$

e$.$ Edge $(i,j)$ is added to $T$ before edge $(g,l).$