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 different three-letter words or codons that can be formed using the four bases adenine, cytosine, guanine, and thymine. This can be calculated using the counting principle: Total number of possible three-letter words = 4 × 4 × 4 = 64.

Step-by-step solution

Understand the counting principle

In this exercise, we have to find the total number of possible three-letter words or codons that can be formed using the four bases given. To solve this problem, we can use the counting principle, which states that if there are n ways to do one task and m ways to do another task, then there are n × m ways to do both tasks.

Apply the counting principle to the problem

There are four bases – adenine, cytosine, guanine, and thymine. Since there are three positions in a codon, we can apply the counting principle to find the total number of possible three-letter words. For the first position, we can choose any of the four bases. Therefore, there are 4 different possibilities for the first position. Similarly, for the second position, we can choose any of the four bases. So, there are again 4 different possibilities for the second position. And for the third position, we can again choose any of the four bases, which means there are 4 different possibilities for the third position as well.

Calculate the total number of three-letter words

Applying the counting principle, we can find the total number of possible three-letter words or codons as follows: Total number of possible three-letter words = Number of possibilities for the first position × Number of possibilities for the second position × Number of possibilities for the third position Total number of possible three-letter words = 4 × 4 × 4 Total number of possible three-letter words = 64 Hence, there are 64 different possible three-letter words or codons that can be formed using the four bases of DNA.