Answer
$25,200$ DNA sequences.
Work Step by Step
Total: $3+2+2+3=10$ letters.
It is a Permutations with Nondistinct Letters:
$\frac{10!}{3!\times2!\times2!\times3!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{6\times2\times2\times6}=\frac{3,628,800}{144}=25,200$