Tetrapeptide is made of naturally occuring alanine , serine, glycine and valine . If the C-terminal amino acid is alanine and the N-terminal amino acid is chiral , the number of possible sequences of the tetrapeptide is

Options

A. 12
B. 8
C. 6
D. 4

Explanation

To determine the number of possible sequences of the tetrapeptide made of alanine (A), serine (S), glycine (G), and valine (V) with specific conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fixed Positions**:
- The C-terminal amino acid is fixed as alanine (A).
- The N-terminal amino acid must be chiral. The chiral amino acids among the given options are alanine (A), serine (S), and valine (V). Glycine (G) is achiral and cannot be at the N-terminal.

2. **List the Possible N-terminal Amino Acids**:
- Since alanine (A) is already at the C-terminal, the possible chiral amino acids for the N-terminal are:
- Serine (S)
- Valine (V)

3. **Determine the Remaining Positions**:
- After fixing the N-terminal and C-terminal, we have two positions left to fill with the remaining amino acids.
- If we choose serine (S) as the N-terminal, the remaining amino acids to arrange in the two middle positions are glycine (G) and valine (V).
- If we choose valine (V) as the N-terminal, the remaining amino acids to arrange in the two middle positions are glycine (G) and serine (S).

4. **Count the Arrangements**:
- For each choice of N-terminal:
- If N-terminal is S: The two remaining positions can be filled with G and V, which can be arranged in 2! (factorial of 2) ways.
- If N-terminal is V: The two remaining positions can be filled with G and S, which can also be arranged in 2! ways.
- Therefore, for each N-terminal choice, there are 2 arrangements.

5. **Calculate Total Arrangements**:
- Since there are 2 choices for the N-terminal (S or V) and each choice allows for 2 arrangements of the remaining amino acids, the total number of possible sequences is:
\[ 2 \text{ (N-terminal choices)} \times 2 \text{ (arrangements)} = 4 \text{ possible sequences.} \]

### Final Answer:
The number of possible sequences of the tetrapeptide is **4**.