This should be a simple one compared to the rest of the problems on this list. Think of the big string as a word, and each number as a letter. Then this is a simple word problem with repeated values. Since there are 20 total letters and repeated multiplicities of 2,4,3,1,2,3,2,3 respectively, therefore the answer is:
$ \frac{20!}{2!\times 4! \times 3! \times 1! \times 2! \times 3! \times 2! \times 3!} $
