Suppose a sequence of 8 nucleotides contains 2 each of a, c, g, t. how many such sequences are there?

The answer is 2520. Suppose that n items are divided into two or more categories, the formula for the combinations of n items is n factorial over the product of the factorial of the number of item in each category. In our case, 8 nucleotides are divided into 4 categories a, c, g, t, and the number of items in each category is 2, so the answer is 8!/(2!*2!*2!*2!)=2520.