Question

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?

Answer 1

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 $4\times 4 = 16$ differents sequences (for example, AA, AG, TT, TG, CT...).

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

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

Therefore, there are $4^{29}$ DNA sequences with exactly 29 letters long.

I hope I've helped you. =D

Enjoy your studies. \o/