The number of tripeptides formed by three different amino acids using each amino acid once is ______.

Solution

Chemistry ma’am · 4 steps

A peptide runs from N-end to C-end, so each new order of the three amino acids is a new tripeptide.

1. Order matters. A peptide has a free -NH₂ group at one end (N-terminal) and a free -COOH group at the other (C-terminal). So Gly-Ala-Val and Val-Ala-Gly are different compounds, not the same molecule written backwards.
2. Fill three positions. Call the amino acids A, B and C. Any of the 3 can sit at the N-terminal, then 2 are left for the middle, and 1 for the C-terminal.

   3 × 2 × 1 = 3! = 6

3. List them. A-B-C, A-C-B, B-A-C, B-C-A, C-A-B and C-B-A. Each one is a different tripeptide.
4. So. Three different amino acids, each used once, give 6 tripeptides.

The common slip: 3. Treating A-B-C and C-B-A as the same chain gives 3, but the N-terminal and C-terminal ends are different, so the two are different tripeptides.

The idea to keep. Peptides are directional, so count arrangements, not selections. With n different amino acids each used once, you get n! peptides.

Answer from the NTA final answer key. Solution by PrepWiser.