1. In some cases, a trait is determined by multiple alleles interacting. In rabbits, coat color is one of those traits. There are four alleles for coat color, each of which causes a different phenotype. Examine the table below and answer the question.

\begin{tabular}{|l|l|l|}
\hline
Phenotype & Allele & Pattern of Inheritance \\
\hline
Dark gray coat & [tex]$C$[/tex] & Dominant to all other alleles \\
\hline
Chinchilla & [tex]$c^{\text{ch}}$[/tex] & Dominant to Himalayan and to white \\
\hline
Himalayan & [tex]$c^{h}$[/tex] & Dominant to white \\
\hline
White & [tex]$c$[/tex] & Recessive \\
\hline
\end{tabular}

A Himalayan and a chinchilla mate, and some of the resulting offspring are white. What must the genotypes of the parents be?

A. [tex]$c^{\text{ch}}c$[/tex] and [tex]$cc$[/tex]
B. [tex]$c^{h}c$[/tex] and [tex]$c^{h}c$[/tex]
C. [tex]$c^{\text{ch}}c^{\text{ch}}$[/tex] and [tex]$cc$[/tex]



Answer :

To determine the genotypes of the parents that result in some white offspring, we need to consider the inheritance patterns of the alleles involved and the fact that for an offspring to be white, it must inherit two recessive white alleles (`c` and `c`). Let's analyze this step-by-step:

1. A white offspring must have the genotype `cc`, since the white allele is recessive.

2. For the offspring to inherit this genotype, each parent must contribute one `c` allele.

3. We are given that one parent is Himalayan and the other is Chinchilla.

4. The genotype for a Himalayan rabbit is either `c^h c` or `c^h c`, but for the purposes of obtaining a white offspring, let's consider the most straightforward one, `c^h c`.

5. The genotype for a Chinchilla rabbit can be either `c^ch c`, but since we've already seen that the white offspring must inherit a `c` allele from each parent, this makes `c^ch c` the appropriate genotype.

Given these points, the possible genotypes for the parents should be:

- The Himalayan parent must have the genotype `c^h c` to pass the recessive `c` allele.
- The Chinchilla parent must have the genotype `c^ch c` to also pass the recessive `c` allele.

Hence, the genotypes of the parents that allow for the possibility of having white offspring are:

[tex]\[ \boxed{c^{\text{h}} c \text{ and } c^{\text{ch}} c} \][/tex]

This thorough approach confirms the result:

- The Himalayan parent has a genotype of [tex]\( c^h c \)[/tex]
- The Chinchilla parent has a genotype of [tex]\( c^{ch} c \)[/tex]

These genotypes ensure that the resulting offspring can be white, fitting all the criteria described.

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