Probability question

Two molecules of Type A, two of type B, two of type C and two of type D are linked together to form a chain molecule. One such chain molecule is ABCDABCD, and another is BCDDAABC. How many molecules would there be if each were indistinguishable?

I think this essentially means how many ways are there to arrange the letters in the word "ABCDABCD" using all the letters.
This would be 8! (8 letters for the first one * 7 remaining for the second one * 6 remaining for the next one, etc * 3 * 2 * 1)
This would be 40320.
However, there are 2 As. Essentially ABCDA (a simpler case) would have 120 ways, even though if we put the first A there, or the second A there it doesn't really matter. Hence we would divide by 2. Notice that there are 4 repeats of 2. This would mean that we divide by 2 four times to get an answer of:
2520.
The answer is 2520. Hope this helps.