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Proteins can take on a wide range of structures and serve a wide range of functions. Much of this structural diversity is due to the fact that any of the 20 different biologically relevant amino acids may be found at any location within the protein.

In 1953, Stanley Miller published a paper detailing his procedure of abiotically producing amino acids and small organic acids from simpler molecules in an apparatus mimicking the conditions of early pre-life Earth. He documented the production of five different amino acids.

How many different polypeptides that are each 10 amino acids long could be made from just these five amino acids?


$5 \times 10 = 50 \text{ polypeptides}$


${10}^{5} = 100,000 \text{ polypeptides}$


${5}^{10} = 9,765,625 \text{ polypeptides}$


$5 \times 4 \times 3 \times 2 \times 1 = 120 \text{ polypeptides}$


$5 + 4 + 3 + 2 + 1 = 15 \text{ polypeptides}$

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