-------ASIDE------------------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
----ONTO THE QUESTION--------------------

We want to arrange A, A, A, B, B, C, and D
There are 7 letters in total
There are 3 identical A's
There are 2 identical B's
So, the total number of possible arrangements = 7!/[(3!)(2!)
= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1)(2)(1)
= (7)(6)(5)(4)/(2)(1)
= (7)(6)(5)(2)
= 420

Answer: C

Cheers,
Brent