Question 1174425: Adenine (A), cytosine (C), thymine (T) and guanine (G) are four main nucleobases found in nucleic acid DNA. DNA has a familiar double helix structure and technologies that sequence DNA first separate the double helix into 2 single sequences (chains), then “read” a single sequence using different strategies. We have 3 locations on one of the single chains of {A, C, T, G}. First one is made up of 3 nucleobases, second one is made up out of 4 and the third one is of length 2 (made up of two nucleobases). If repetitions are allowed within a single location (for example, at the first location, you can’t have AAA or TAT etc. ) how many different DNA sequences can we make, if we concatenate (put first, second, and third location consecutively next to each other) the three locations. (HINT1: Take a look at visualization of the concepts “location”, “length” etc. beneath. HINT2: Sequences are different if the order and/or content of nucleobases is different between them. )
DNA sequence of length 22 with a dummy nucleobase N (any N can be exchanged by some A,C, T or G):
N N N (N N N) N N (N N N N) N N N (N N) N N N N N
N’s in parenthesis are 3 locations, first, second and third respectively from left to right. Within a single location you can have repetitions of nucleobases. We are interested in the number of different length 9 sequences that we can make by concatenating the three locations.
(Please just write the final number that you calculate no words, no expressions, just the final result which is to be a positive integer!)
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Thank you for detailed description of these molecular biology basics.
Mathematicians never think in these terms.
So, I will edit the problem in a way, as mathematicians do it.
So, we have the words of the length of 9, written in the 4-letter alphabet A, C, T, G, where repetition is allowed.
The question is how many such 9-letter words are possible ?
The answer is  , since in each of 9 positions we have 4 independent possibilities.
Solved.
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It is interesting to me to know from you, if I correctly translated your problem to Math --- PLEASE respond.
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