Question

How many tripeptides could one make from glycine, valine, and lysine, using any number of each amino acid?

Short answer

Answer: There are 27 possible tripeptides that can be made using any number of glycine, valine, and lysine amino acids.

Step-by-step solution

Understand the context

In this problem, we are given three amino acids: glycine (G), valine (V), and lysine (K). We need to create a tripeptide, which means forming a combination of these amino acids in a sequence of length three. We're allowed to use any number of each amino acid, so repetitions are allowed.

Apply the permutation formula

Since the tripeptide consists of three positions and there are three amino acids that can occupy each position, we can use the permutation formula to determine the number of possible combinations. The permutation formula in this case can be represented as n^r, where 'n' is the number of amino acids and 'r' is the number of positions in the tripeptide. In this case, we have: n=3 (glycine, valine, lysine) r=3 (three positions in the tripeptide)

Calculate the number of tripeptides

Using the permutation formula given above (n^r), we can now calculate the number of possible tripeptides: 3^3 = 3*3*3 = 27 tripeptides There are 27 possible tripeptides that can be made using any number of glycine, valine, and lysine amino acids.