There are 36 possible genotypes for an autosomal gene with 8 alleles. How many genotypes will be possible for an X-linked gene with 8 alleles?

Options

A. 18
B. 36
C. 44
D. 72

Explanation

To solve the problem of determining how many genotypes are possible for an X-linked gene with 8 alleles, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Genotypes for Autosomal Genes:**
- For an autosomal gene with multiple alleles, the formula to calculate the number of possible genotypes is given by:
\[ \text{Number of Genotypes} = \frac{N(N + 1)}{2} \]
- Here, \(N\) is the number of alleles. For the autosomal gene with 8 alleles:
\[ N = 8 \]
- Plugging in the value:
\[ \text{Number of Genotypes} = \frac{8 \times (8 + 1)}{2} = \frac{8 \times 9}{2} = \frac{72}{2} = 36 \]

2. **Understanding Genotypes for X-linked Genes:**
- For an X-linked gene, the situation is slightly different because males have one X and one Y chromosome, while females have two X chromosomes.
- For females (XX), the number of genotypes can be calculated using the same formula as above:
\[ \text{Number of Genotypes for Females} = \frac{8 \times (8 + 1)}{2} = 36 \]
- For males (XY), since they only have one X chromosome, the number of possible genotypes is simply equal to the number of alleles:
\[ \text{Number of Genotypes for Males} = 8 \]

3. **Combining Genotypes:**
- To find the total number of genotypes for the X-linked gene, we need to combine the genotypes from both males and females:
\[ \text{Total Genotypes} = \text{Genotypes from Females} + \text{Genotypes from Males} \]
\[ \text{Total Genotypes} = 36 + 8 = 44 \]

4. **Conclusion:**
- Therefore, the total number of possible genotypes for an X-linked gene with 8 alleles is **44**.