Question

Proteins are made up of chains of amino acids. Insulin is a relatively small protein with 53 amino acid residues. How many possible proteins of length 53 can be made with 20 possible amino acids for each position in the protein?​

Answer 1

Given:

Possible length = 53

Possibility for each position = 20

To find:

How many possible proteins can be made ?

Solution:

This problem is nothing but selection problem in which there are 53 positions and each position has 20 possible options in which repetition is allowed.

Number of possible options for 1st position = 20

Number of possible options for 2nd position = 20

Number of possible options for 3rd position = 20

Number of possible options for 4th position = 20

:

:

Number of possible options for 52nd position = 20

Number of possible options for 53rd position = 20

Therefore, total number of possible proteins = 20 $\times$20$\times$ 20 $\times$ .... 53 times

i.e. the answer is: $\bold{20^{53}}$