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A DNA sequence can be represented as a string of the letters ACTG (short for adenine, cytosine, guanine, and thymine). How many DNA sequences are exactly 29 letters long?

Respuesta :

RiskeMauri

To solve that question we can think by the following way:

  • The first letter can be any of the letters (A, C, T or G). Therefore there are 4 possibilites.
  • To choose the second letter of the sequence, any letter also can be chose. So, one more time, there are 4 possibilites.

Using the fundamental principle of counting, we will find out that can be formed [tex]4\times 4 = 16[/tex] differents sequences (for example, AA, AG, TT, TG, CT...).

Know we know that, we can generalize. If I have [tex]n[/tex] elements and I must choose one of them [tex]t[/tex] times to do a sequence, the total number of sequence that I can form will be [tex]n^t[/tex].

In our question, we want to know how many DNA sequence are exactly 29 letters long. As indicated above, the answer for that is [tex]4\times 4\times 4\times ... \times 4[/tex] (29 times) [tex]= 4^{29}[/tex].

Therefore, there are [tex]4^{29}[/tex] DNA sequences with exactly 29 letters long.

I hope I've helped you. =D

Enjoy your studies. \o/

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