# How many possible codons?

Consider a codon of the form NNK (where N = Adenine, Cytosine, Guanine or Uracil & K = Uracil or Guanine). How many codons are now available? I know if all were available there would be 4^3 = 64 codons. How many are possible now? When I have tried combinations manually I got it to be 32, is this correct?

• 4 * 4 * 2 = 32.
– user24284
May 9 '17 at 11:35
• What is being meant by N and NN of NNK? Does it means the first 2 nucleotides have to be same? May 9 '17 at 11:43

Yes, 32 is correct.

Technically, I have nothing to add what Gerardo Furtado and a tiger haven't already mentioned but a graphical representation of all permutations might help to understand this a bit better.

For the first 2 positions in the codon we have 4 bases to choose from (adenine, guanine, uracil and cytosine). So this can mathematically be represented as 4 x 4 = 16 or visually as: Now, for the next position (the position of interest) we only have two bases to choose from (uracil and guanine). Leaving us with 4 x 4 x 2 = 32 different permutations, or visually: • You are welcome. I am glad it helped. May 10 '17 at 12:01

Yes, it is.

• Good explanation. For completeness, it would be extremely unusual if NNK denoted that the first two bases had to be identical: first off, it’s not the convention; IUPAC ambiguity codes are character wildcards, not variables in the common mathematical sense. And secondly, there’s little biological reason to consider codons where the first two bases are identical. May 9 '17 at 16:21