Human genetic material (DNA) is made up of sequences of the molecules adenosine (A), guanine (G), cytosine (C), and thymine (T), which are called bases. A codon is a sequence of three bases. Replicates are allowed, so AAA, CGC, and so forth are codons. Codons are important because each codon causes a different protein to be created.

a. How many different codons are there?

b. How many different codons are there in which all three bases are different?

c. The bases A and G are called purines, while C and T are called pyrimidines. How many different codons are there in which the first base is a purine and the second and third are pyrimidines?

d. What is the probability that all three bases are different?

e. What is the probability that the first base is a purine and the second and third are pyrimidines?