Our genetic material, DNA, is formed from a $4$ letter alphabet" of bases: A, T, G, C (adenine, thymine, guanine, and cytosine). The order in which the letters are arranged is important, but because a molecule can move, there is no difference between a sequence and the same sequence reversed. How many distinct DNA sequences of $5$ bases are there?
The only bit I've gotten so far is $4^5$ I have no idea how to start with the palindrome. Can anyone walk me through on the thought process please?