Total number of tripeptides possible by mixing of valine and proline is ___________

Solution

Chemistry ma’am · 4 steps

Three positions in the chain, two choices for each position: that is 2 × 2 × 2.

1. Order matters. A peptide chain has a free -NH₂ end (N-terminus) and a free -COOH end (C-terminus). So Val-Val-Pro and Pro-Val-Val are different tripeptides, and each sequence counts separately.
2. Fill three positions. Each of the three positions can hold valine (V) or proline (P), and an amino acid may repeat. So each position has 2 choices.

   2 × 2 × 2 = 2³ = 8

3. List them. VVV, VVP, VPV, PVV, VPP, PVP, PPV, PPP. That gives 8 sequences, including the two that use only one amino acid.
4. So. The total number of tripeptides possible is 8.

The common slip: 6. Counting only tripeptides that contain both valine and proline leaves out VVV and PPP and gives 6, not 8.

The idea to keep. With n different amino acids, repeats allowed, you can make nᵏ peptides of length k. Sequence direction matters, so do not merge reversed chains.

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