Chapter 15.5, Problem 18WE

To determine

To calculate: The number of different sequences of A, T, C and G that can be arranged along a strand of DNA with 8 base units.

Answer to Problem 18WE

The number of different sequences of A, T, C and G that can be arranged along a strand of DNA with 8 base units are $65536$ .

Explanation of Solution

Given information:

In a DNA molecule the base units are adenine A, thymine T, cytosine C and guanine G. A sequence with help of these molecules is to be formed such that the DNA has 8 base units.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that in a DNA molecule the base units are adenine A, thymine T, cytosine C and guanine G. A sequence with help of these molecules is to be formed such that the DNA has 8 base units.

Let DNA with 8 base unitsbe $\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\text{}\boxed{}\boxed{}$ .

For each unit there are 4 choices among adenine A, thymine T, cytosine C and guanine G.

So each base of 8 base unit of DNA is filled with any 1 of 4molecules.

  $\boxed{4}\boxed{4}\boxed{4}\boxed{4}\boxed{4}\boxed{4}\boxed{4}\boxed{4}$

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $\begin{array}{c}4\times 4\times 4\times 4\times 4\times 4\times 4\times 4=4^8\\ =65536\end{array}$

Thus, the number of different sequences of A, T, C and G that can be arranged along a strand of DNA with 8 base units are $65536$ .