# How many distinct 55-amino-acid sequences are there?

Recall that there are 64 different 3-letter combinations of nucleotides, but only 20 amino acids. Furthermore, you know that the first codon in the sequence has to be a start codon, and the last one has to be a stop codon.

### So, how many distinct amino acid sequences are there?

(To make this problem interactive, turn on javascript!)

- I need a hint ... : How many amino acids in the peptide? 165/3 = 55, minus the start and stop makes 53.

- ...another hint ... : Apply the combine-by-multiplying rule 53 times... or use the shortcut.

#### I think I have the answer: 20^53 = 9.00 × 10^{68}.

So, there are 2.19 × 10^{99} distinct 165-nucleotide sequences, but only 9.00 × 10^{
68} distinct 53-amino-acid peptides. That's a big difference, and suggests a lot of repetition in DNA.

**On average, how many ways can each 53-peptide sequence be coded? **

If you don't want to do problems like the above, you will need to know how to divide numbers in scientific notation!

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