Step 1: Understanding the Concept:
Polypeptide diversity is governed by the combinations of the 20 standard amino acids.
The genetic code consists of 64 triplet codons, which code for amino acids or act as translation termination signals.
Step 2: Detailed Explanation:
Let us evaluate each statement independently.
- Statement (I) states that there are \( 20^{146} \) possible sequences for a polypeptide of 146 amino acids.
For a polypeptide of length \( n \), with 20 different possible amino acids at each position, the total possible unique sequences is:
\[ \text{Total sequences} = 20^n \]
For \( n = 146 \), the value is indeed \( 20^{146} \).
Thus, Statement (I) is correct.
- Statement (II) states that four triplets do not code for any amino acid.
The genetic code contains 64 triplet codons.
Among these, 61 codons are coding codons that specify amino acids.
The remaining 3 codons are stop codons: UAA, UAG, and UGA.
These three stop codons do not code for any amino acid; instead, they signal the termination of translation.
Therefore, only three triplets (not four) do not code for any amino acid.
Thus, Statement (II) is incorrect.
Step 3: Final Answer:
Statement (I) is correct but Statement (II) is incorrect, corresponding to option 3.