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Chapter 18: Problem 53

How many different tetrapeptides can be made from two alanines and two glycines?

Short Answer

Expert verified
There are 6 different tetrapeptides that can be made from two alanines (A) and two glycines (G). This can be calculated using the combination formula, \(C(4, 2) = \frac{4!}{2!2!} = 6\).

Step by step solution

01

Counting possible tetrapeptides

To find the total number of tetrapeptides that can be made from two alanines (A) and two glycines (G), we will be counting the distinct ways to arrange these amino acids.
02

Arranging amino acids

Four positions to be filled by the amino acids Alanine (A) and Glycine (G) are as follows: _ _ _ _. Since we have two of each amino acid, we need to consider all the possible unique arrangements that can be made by placing Alanines and Glycines in different positions.
03

Calculating combinations

To find different tetrapeptides (unique arrangements), we can think about choosing two positions out of four to put alanines (and the remaining two positions will have glycines). We will use the combination formula: \[C(n, r) = \frac{n!}{r!(n-r)!}\] Here, C(n, r) represents the number of combinations that can be made by choosing r elements from a set of n elements, n! is the factorial of n, and r! is the factorial of r. For this problem: - n = 4 (total positions of the amino acids) - r = 2 (number of alanines to be placed in the positions) So, \[C(4, 2) = \frac{4!}{2!(4-2)!}\]
04

Solving the combination formula and finding the answer

Plugging the values of n and r into the combination formula, we get: \[C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4!}{2!2!} = \frac{4 \times 3 \times 2 \times 1}{(2 \times 1)(2 \times 1)} = \frac{24}{4} = 6\] Hence, there are 6 different tetrapeptides that can be made from two alanines and two glycines.

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