To solve the problem of determining the proportion of progeny that will genotypically resemble the first parent in the cross AaBbCcDdEe x aaBbccddee, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Genotypes of the Parents:**
- Parent 1: AaBbCcDdEe (heterozygous for all genes)
- Parent 2: aaBbccddee (heterozygous for B only, recessive for the others)
2. **Determine the Gametes Produced by Each Parent:**
- For Parent 1 (AaBbCcDdEe):
- Each gene can contribute either a dominant (A, B, C, D, E) or recessive (a, b, c, d, e) allele.
- The number of different gametes can be calculated using the formula \(2^n\), where \(n\) is the number of heterozygous gene pairs.
- Here, \(n = 5\) (A, B, C, D, E), so the number of gametes = \(2^5 = 32\).
- For Parent 2 (aaBbccddee):
- The only heterozygous gene is B, which can contribute either B or b.
- The other genes (A, C, D, E) can only contribute recessive alleles (a, c, d, e).
- Thus, the number of gametes = 2 (B or b).
3. **Calculate the Total Number of Offspring Combinations:**
- The total number of combinations in the Punnett square is the product of the number of gametes from both parents.
- Total combinations = \(32 \text{ (from Parent 1)} \times 2 \text{ (from Parent 2)} = 64\).
4. **Identify the Desired Genotype:**
- We want the genotype to resemble Parent 1 (AaBbCcDdEe), which means we need to have:
- A (dominant from Parent 1)
- B (can be either B or b from Parent 2)
- C (dominant from Parent 1)
- D (dominant from Parent 1)
- E (dominant from Parent 1)
5. **Determine the Successful Combinations:**
- The successful combinations that yield AaBbCcDdEe are:
- From Parent 1 gamete: A (dominant), B (dominant), C (dominant), D (dominant), E (dominant).
- From Parent 2 gamete: aa (recessive), Bb (heterozygous), cc (recessive), dd (recessive), ee (recessive).
- The only combinations that yield the desired genotype are:
- 1. A from Parent 1, B from Parent 2, C from Parent 1, D from Parent 1, E from Parent 1.
- 2. A from Parent 1, b from Parent 2, C from Parent 1, D from Parent 1, E from Parent 1.
- Therefore, there are 2 successful combinations that yield the desired genotype.
6. **Calculate the Proportion:**
- Proportion of progeny resembling Parent 1 = \(\frac{\text{Number of successful combinations}}{\text{Total combinations}} = \frac{2}{64} = \frac{1}{32}\).
### Final Answer:
The proportion of the progeny that will genotypically resemble the first parent is **1/32**.
