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# A trihybrid cross is made between two plants with genotype $\dfrac{A}{a} \dfrac{B}{b} \dfrac{C}{c}$, how many offsprings of such cross will have a genotype $\dfrac{a}{a} \dfrac{b}{b} \dfrac{c}{c}$?A. $\dfrac{1}{64}$B. $\dfrac{1}{4}$C. $\dfrac{1}{16}$D. $\dfrac{1}{32}$

Last updated date: 20th Jul 2024
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Hint: Genetics is a branch of biology which deals with the inheritance as well as the variation of characters from parents to offspring.
Inheritance is the process by which characters are passed on from one generation to another generation.

Genetics is the study of hereditary (Transmission of characters from parents to offspring).
George Mendel conducted hybridization experiments on garden peas for seven years and proposed the laws of inheritance in living organisms.

He gave three laws:
1. Laws of segregation.
2. Law of independent assortment
3. Law of dominance.

- Genes: Genes are the unit of inheritance.
- Alleles: Genes which code for a pair of contrasting traits.
- Monohybrid cross: A monohybrid cross is defined as the cross happening in the F1 generation offspring of parents differing in one trait only.
- Dihybrid cross: A dihybrid cross is a cross that happens to F1 generation offspring of differing two traits.
- Trihybrid crosses: An individual or strain that is heterozygous for three pairs of genes.
For example: $AaBbCc \times AaBbCc.$

So, according to the question If we consider a cross between AaBbCc, the value of $n = 3$.
The maximum number of possible gametes is 2 raised to 'n'.
Value of $n = 3$.
Thus, maximum $2 \times 2 \times 2 = 8$ gametes are produced.

This makes it clear that the maximum offspring produced is $8 \times 8 = 64$. The possibility of a recessive genotype in this combination of Punnett square is $\dfrac{1}{64}$.
This means that one out of 64 offspring produced will have aabbcc genotype.

Hence, The correct answer is option (A).

Note: Law of segregation: It states that during gamete formation, the two alleles at a gene locus segregate from each other; each gamete has an equal probability of containing either allele.
Law of independent assortment: It states that genes for different traits assort independently of one another in the formation of gametes.
Law of dominance: It states that in a heterozygote, one trait will conceal the presence of another trait for the same characteristic.