Question

Problem 1. DNA sequences consist of four letters (also called bases): A, T, C, and G. The DNA sequences of humans have approximately 4 billion bases (4 x 10). How many possible DNA sequences of length 4 billion are there?

Answer 1

Each of the base in a DNA sequence of length 4 billion can be chosen in 4 ways, namely A, T, C or G.

Moreover, the choice of a base doesn't affect the other bases.

Thus, there are a total of 4^(4 billion) = 4^(4*10⁹)possible DNA sequences of length 4 billion.

OR

The first base in the DNA sequence can be chosen in 4 ways (A, T, C or G).

The second base in the DNA sequence can be chosen in 4 ways (A, T, C or G).

The third base in the DNA sequence can be chosen in 4 ways (A, T, C or G).

...

...

The (4*10⁹)th base in the DNA sequence can be chosen in 4 ways (A, T, C or G).

$\begin{align*} \text{Thus, total no. of possible DNA sequences of length 4 billion} &= 4*4*4*...*4 \ \ \ \ \text{(4 billion times)} \\ &= 4^{\text{4 billion}} \\ &= \mathbf{4^{4*10^9}} \ \ \ \ \ \textbf{[Answer]} \end{align*}$

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