Question

The codons (words) in DNA (that specify which amino acid should be at a particular point in a protein) are three bases long. How many such three- letter words can be made from the four bases adenine, cytosine, guanine, and thymine?

Short answer

There are 64 possible unique three-letter codons that can be made from the four DNA bases adenine, cytosine, guanine, and thymine. This is calculated as \(4 * 4 * 4 = 64\).

Step-by-step solution

Identify the total elements and possible combinations

There are four DNA bases: adenine (A), cytosine (C), guanine (G), and thymine (T). We need to find out how many unique three-letter words (codons) can be made from these bases. In each position within a codon, any of the 4 bases can be placed.

Find the total number of combinations for each position

Since there are 4 bases, and each position can have any of the 4 bases, we can say that there are 4 options for each position in the codon.

Calculate the total number of possible codons

To find the total number of combinations, we multiply the number of combinations for each position. In this case, we have 4 combinations for the first position, 4 combinations for the second position, and 4 combinations for the third position. So the total number of possible codons is: \(4 * 4 * 4 = 64\)

Determine the final answer

By applying the combinatorics principles, we found out that there are 64 possible unique three-letter codons that can be made from the four DNA bases adenine, cytosine, guanine, and thymine.