# 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, 2017 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, 2017 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, 2017 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, 2017 at 16:21