In a trihybrid cross, the different types of genotypes obtained in the `F_2` generation is

Options

A. 8
B. 18
C. 27
D. 36

Answer

To solve the problem regarding the number of different genotypes obtained in the F2 generation of a trihybrid cross, we can follow these steps:

### Step 1: Understand the Trihybrid Cross
A trihybrid cross involves three different traits, each represented by a different gene. For example, we can denote these traits as A, B, and C. Each trait can have two alleles (dominant and recessive).

### Step 2: Determine the Number of Alleles
Since each trait has two alleles, for three traits (A, B, and C), we have:
- Trait A: 2 alleles (A and a)
- Trait B: 2 alleles (B and b)
- Trait C: 2 alleles (C and c)

### Step 3: Calculate the Total Number of Genotypes
To find the total number of genotypes in the F2 generation, we can use the formula for the number of genotypes in a dihybrid or trihybrid cross. The formula is:
\[ \text{Number of Genotypes} = (n + 1)^k \]
where \( n \) is the number of alleles for each trait (which is 1 for dominant and 1 for recessive, so \( n = 1 \)), and \( k \) is the number of traits.

For a trihybrid cross:
- \( n = 1 \) (for each trait)
- \( k = 3 \) (three traits)

Thus, the calculation becomes:
\[ \text{Number of Genotypes} = (2)^3 = 8 \]

However, this only accounts for the combinations of alleles. To find the total distinct genotypes, we need to consider the combinations of the three traits.

### Step 4: Calculate Distinct Genotypes
For a trihybrid cross, the total number of distinct genotypes can also be calculated as:
\[ \text{Distinct Genotypes} = \frac{(2n)^k}{2} \]
where \( n \) is the number of traits (3 in this case), and \( k \) is the number of alleles per trait (2).

Thus, we calculate:
\[ \text{Distinct Genotypes} = \frac{(2^3)}{2} = 27 \]

### Conclusion
In a trihybrid cross, the number of different genotypes obtained in the F2 generation is 27.