To understand the number of tripeptides formed by three different amino acids using each amino acid once, consider the amino acids as distinct objects we need to arrange. In this case, we have 3 amino acids (let’s name them A, B, and C for simplicity). The question asks how many unique sequences (tripeptides) we can form if we use each amino acid exactly once.

Arranging 3 distinct items in a sequence is a fundamental combinatorial problem. The number of ways to arrange n distinct objects is given by the factorial of n, denoted as n!. The factorial function (n!) means multiplying all whole numbers from n down to 1. Therefore, for 3 amino acids, the number of unique tripeptides we can form is calculated by 3! (3 factorial).

3! = 3 × 2 × 1 = 6

This means there are 6 possible unique tripeptides that can be formed using these three different amino acids exactly once, which are: ABC, ACB, BAC, BCA, CAB, CBA.