Number of peptides = (Number of amino acids)! / (Number of duplicate amino acids!)
In this case, we assume that we have 20 different amino acids and each amino acid is used only once. Therefore, the number of duplicate amino acids is 0.
Number of peptides = (20!) / (0!)
The factorial of 0 is defined as 1, so we get:
Number of peptides = 20! / 1
20! can be calculated by multiplying all integers from 1 to 20:
20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
The result of this multiplication is a very large number:
20! = 2,432,902,008,176,640,000
Therefore, the number of different peptides that can be formed by using all 20 amino acids only once is 2,432,902,008,176,640,000.
