The letters A B C D E are arranged randomly in a line. In how many arrangements is the letter A in front of D?

Any idea how I can do this? I was thinking of drawing out all possible cases, but is there a faster way that can be used to generalize to a large number of unique items?

Right now I have :

A L L L D = 3!

L A L L D = $^3C\_2 \cdot 2$

L L A L D = $^3C\_2 \cdot 2$

L L L A D = 3!

So total there are 24 possible arrangements. Am I on the right track?