How many different amino acid sequences are possible in a polypeptide 146 amino acids long?
\(20^{146}\)
Proteins are built from 20 standard amino acids. In a polypeptide of length n, each of the n positions can be occupied independently by any one of the 20 amino acids.
By the multiplication rule of counting, the total number of distinct sequences equals 20 multiplied by itself n times, that is 20^n. For a chain of 146 residues, n = 146, giving 20^146 possible sequences. The other options either linearly multiply the two values or interchange the base and exponent, which does not reflect independent selection at each position.
Hence, the number of different amino acid sequences possible in a polypeptide 146 residues long is 20^146.
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