Thread: [SOLVED] Using Product Rule for Discrete Math

1. [SOLVED] Using Product Rule for Discrete Math

The question is
A sequence is palindromic if it is unaltereld when read in reverse order. How many palindromic sequences of length 6 are there in the 4 letter code T, A, G, C?

I know the answer is 64, Just not sure how to do it.
(6-4)^6 gives me the right answer, but it just doesn't seem to be right. Any help would be greatly appreciated. Thanks.

2. 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}?

$\text{We have:} \;\;_{\begin{array}{cccccc} \_\_ & \_\_ & \_\_ & \_\_ & \_\_ & \_\_ \\
^1 & ^2 & ^3 & ^4 & ^5 & ^6
\end{array}}$

Since it is a palindrome, it will be of the form: . $X\,YZZ\,YX$
. . 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: . $4^3 \,=\,64$ possible palindromes.