## Related questions with answers

DNA molecules consist of chemically linked sequences of the bases adenine, guanine, cytosine, and thymine, denoted A, G, C, and T. A sequence of three bases is called a codon. A base may appear more than once in a codon. a. How many different codons are there? b. The bases A and G are purines, while C and T are pyrimidines. How many codons are there whose first and third bases are purines and whose second base is a pyrimidine? c. How many codons consist of three different bases?

Solution

Verified(a) $\textbf{Fundamental counting principle}$: If the first event could occur in $m$ ways and the second event could occur in $n$ ways, then the number of ways that the two events could occur in sequence is $m\cdot n$.

A codon is a sequence of three bases, while there are four bases (A, G, C, T).

First base: 4 ways

Second base: 4 ways

Third base: 4 ways

Use the fundamental counting principle:

$4\cdot 4\cdot 4=4^3=64$

Thus there are 64 different codons.

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