Problem 106 - Chemistry An Atoms First Approach

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?

Step-by-Step Solution

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 1: 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.

Step 2: 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.

Step 3: 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: \(4 * 4 * 4 = 64\)

Step 4: 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.