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Math Help - [SOLVED] Using Product Rule for Discrete Math

  1. #1
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    [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.
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  2. #2
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    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} \_\_ & \_\_ & \_\_ & \_\_ & \_\_ & \_\_ \\<br />
^1 & ^2 & ^3 & ^4 & ^5 & ^6 <br />
\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.

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