Use the Activity$-$on$-$Arrow $($AOA$)$ diagram on the following page to determine the following $-$each number is the number of hours for the task.

$\backslash$table$[[$a$.$ How many different paths are there through the network?$],[$b$.$ What is the number of the last node in the network?$],[$c$.$ What is the difference in hours taken for the two paths when they$],[$connect at node $10],[$d$.$ What is the difference in hours taken for the two paths when they$],[$connect at node $12.],[$e$.$ What is the expected duration of the entire project?$],[$f$.$ What is the critical path? Separate each node with a dash $(-).]]$

g$.$ Which is the longest path? Separate each node with a dash $(-).$