Hello, smellatron!

A sequence is palindromic if it is unaltereld when read in reverse order.

How many palindromic sequences of length 6 are there with the 4 letters {T,A,G,C}?

Since it is a palindrome, it will be of the form: .

. . and we are concerned with filling the first three spaces.

. . For the 1st space, there are 4 choices.

. . For the 2nd space, there are 4 choices.

. . For the 3rd space, there are 4 choices.

Therefore, there are: . possible palindromes.