How many

different polypeptides of 61 residues can be made from the20

naturally occurring amino acids?

different polypeptides of 61 residues can be made from the 20  naturally occurring amino acids

Explanation:

Considering that there are 20 chemically different amino acids occurring in nature and that each of these 20 variants can be place in any position of a polypeptide sequence, the total variants can be calculated as the total possibilities or combinations of them.

For instance, in the case we have a dipeptide (formed by only two amino acids) one could place any of the 20 amino acids in the first position (20 possibilities) but also any of the same 20 amino acids in the second one.

As one could easily see, the total amount of possibilities results from multiply 20 x 20 = 8,000. Thus one can build 8,000 different combinations of 2 amino acids.

In case we use three amino acids to form a tripeptide, the total amount of different possibilities increases to 20 x 20 x 20 =  160,000.

Thus, one can derive from this reasoning a formula to express the number of possible combination of amino acids for a given number of them.

This formula is

where 20 indicates all the amino acids that can occupy a certain position in the polypeptide's chain and n  represents the chain's length, this is, the total amino acids forming the polypeptide sequence (primary structure).

In our example, one have different polypeptides of 61 residues can be made from the 20  naturally occurring amino acids