EXAMPLE 13 DNA Sequences

A strand of deoxyribonucleic acid (DNA) is a long sequence of the nucleotides adenine, cytosine, guanine, and thymine (abbreviated A, C, G, T). One helical turn of a DNA strand would contain a sequence of 10 of these acids, such as ACTGCCATGT. How many possible sequences of this length are there?

There are 4 letters that can occur in each position in the 10-letter sequence. Any of the 4 letters can be in the first position. Regardless of what is in the first position, any of the 4 letters can be in the second position, and so on. The order of the letters matters, so a sequence that begins AC will be different from one that begins CA. The number of different 10-letter sequences is more than 1 million:

As big as that number is, consider that it would take a DNA sequence about 3 billion letters long to contain your entire genetic “blueprint”!

364

Knowing the number and frequency of DNA sequences has proven important in criminal justice. When skin or bodily fluids from a crime scene are “DNA fingerprinted,” the specific DNA sequences in the recovered material are extremely unlikely to be found in any suspect other than the perpetrator. The counting technique used in this example is expressed as Rule A on page 365.