Type of genotypes in trihybrid cross is

Options

A. 3
B. 9
C. 27
D. 64

Answer

To determine the number of genotypes in a trihybrid cross, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Trihybrid Cross**:
A trihybrid cross involves three traits, each controlled by a different gene. For example, let’s consider genes A, B, and C, where each gene can have two alleles (dominant and recessive).

2. **Calculating the Number of Gametes**:
Each parent can produce gametes that carry combinations of these alleles. Since each gene has two alleles, the number of different gametes produced by each parent can be calculated using the formula \(2^n\), where \(n\) is the number of traits being considered. For three traits (A, B, and C), the number of gametes is:
\[ 2^3 = 8 \]

3. **Setting Up the Punnett Square**:
When we perform a trihybrid cross, we can visualize the combinations of gametes using a Punnett square. Since each parent can produce 8 different gametes, the total number of combinations in the offspring can be calculated as:
\[ 8 \times 8 = 64 \]

4. **Counting Unique Genotypes**:
While there are 64 combinations of gametes, not all of these combinations will result in unique genotypes. The number of unique genotypes can be calculated using the formula \( (n + 1)^k \), where \(n\) is the number of alleles (2 for dominant and recessive) and \(k\) is the number of traits (3 in this case). Thus, we have:
\[ (2 + 1)^3 = 3^3 = 27 \]
This means there are 27 unique genotypes in a trihybrid cross.

5. **Conclusion**:
Therefore, the number of different genotypes that can arise from a trihybrid cross is **27**.

### Final Answer:
The number of genotypes in a trihybrid cross is **27**.

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