Question

How many different pentapeptides can be formed using five different amino acids?

Short answer

There are 120 different pentapeptides that can be formed using the given five amino acids. This is calculated using the permutation formula \(P(n, r) = \frac{n!}{(n-r)!}\), where n is the number of amino acids and r is the number of positions to fill. In this case, \(P(5, 5) = \frac{5!}{(5-5)!} = \frac{120}{1} = 120\).

Step-by-step solution

Define the problem

We need to find the number of ways to arrange five different amino acids to form pentapeptides. Since a pentapeptide has five positions for the amino acids, we will be arranging the five amino acids to fill these positions without repetition.

Permutation formula

The permutation formula, denoted by P(n, r), is a way to find the number of ways to arrange 'n' items in 'r' positions without repetition. The formula is: P(n, r) = n!/(n-r)! In our case, we have 5 different amino acids and 5 positions to fill, so n=5 and r=5.

Calculate the factorial of n and n-r

First, we need to calculate the factorial of 'n' (5) and 'n-r' (0): - 5! = 5 × 4 × 3 × 2 × 1 = 120. - 0! is defined as 1.

Calculate the permutations using the formula

Now, we can calculate P(5, 5) using the formula. P(5, 5) = 120/1 = 120

Write the final answer

There are 120 different pentapeptides that can be formed using the given five amino acids.