Step 1: Understanding codons and degeneracy.
The genetic code consists of codons, which are triplets of nucleotide bases in mRNA. There are 64 possible codons derived from the combination of four bases (A, U, G, C) taken three at a time. Out of these:
61 codons encode amino acids.
3 codons are stop codons (UAA, UAG, UGA) that terminate protein synthesis.
Degeneracy refers to the fact that multiple codons can encode the same amino acid. For example:
Leucine is encoded by six different codons (CUU, CUC, CUA, CUG, UUA, UUG).
Methionine is encoded by only one codon (AUG), showing no degeneracy.
Step 2: Analysis of the options.
Option (A): Incorrect. There are 64 codons, not 20, and not all exhibit degeneracy.
Option (B): Incorrect. Some codons exhibit degeneracy; it is not true that none do.
Option (C): Correct. There are 64 codons, and many of them exhibit degeneracy by encoding the same amino acid.
Option (D): Incorrect. There are 64 codons, not 20, and degeneracy exists.
Step 3: Conclusion.
The correct statement is that there are 64 codons, and some of them exhibit degeneracy.
\[
\therefore \text{The correct answer is: There are 64 codons, and some of them exhibit degeneracy.}
\]