# 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 × 1068.

So, there are 2.19 × 1099 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!