A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is :

<p>To determine the number of tetrapeptide sequences possible using the amino acids glycine (Gly), alanine (Ala), valine (Val), and leucine (Leu), we consider the concept of permutations. Since each tetrapeptide sequence consists of four different amino acids, we need to calculate the number of ways to arrange these four different elements.</p> <p>The formula for the number of permutations of a set of $ n $ distinct elements is given by $ n! $ (n factorial), where $ n! = n \times (n-1) \times (n-2) \times \cdots \times 1 $.</p> <p>For our case:</p> <p>$ n = 4 $</p> <p>Hence, the number of possible sequences (or permutations) is:</p> <p>$ 4! = 4 \times 3 \times 2 \times 1 = 24 $</p> <p>Thus, there are 24 different tetrapeptide sequences possible using each of the four amino acids exactly once.</p>