Combinatorics of the code: With four RNA bases taken three at a time, how many distinct codons exist in the standard genetic code?

Introduction / Context:Codons are triplets of nucleotides formed from four bases (A, U, G, C). Counting possible combinations is a basic question linking combinatorics and molecular biology.

Given Data / Assumptions:

• Four symbols (A, U, G, C).
• Ordered triplets (position matters).
• Repetition allowed.

Concept / Approach:The number of ordered triplets with repetition from a set of four is 4^3. This yields the total number of possible codons recognized by the translation machinery.

Step-by-Step Solution:

Verification / Alternative check:Genetic code tables list 64 entries, confirming the combinatorial calculation.

Why Other Options Are Wrong:

• 3: confuses number of bases with number of codons.
• 20: number of standard amino acids, not codons.
• Infinite: the triplet code yields a finite set of combinations.

Common Pitfalls:Mixing up amino acid count with codon count; forgetting that multiple codons can encode the same amino acid (degeneracy).

Final Answer:64