So I have a problem about inheritance. In single meiosis, random assortment can create 4 different genetically gametes or not ?

Yes, in a single meiosis event, random assortment can indeed create four different genetically unique gametes. Here's a detailed explanation of how this occurs:

1. Break Down the Problem:

   • Meiosis is a type of cell division that reduces the chromosome number by half, resulting in the production of gametes (sperm and eggs).
   • Random assortment refers to the way chromosomes are distributed into gametes independently of one another.

2. Relevant Concepts:

   • Independent Assortment: During meiosis I, homologous chromosomes are distributed randomly into daughter cells. This means that each gamete receives a random mix of maternal and paternal chromosomes.
   • Crossing Over: Although not directly related to random assortment, crossing over during prophase I can further increase genetic variation by exchanging genetic material between homologous chromosomes.

3. Analysis and Detail:

   • Consider a simple organism with two pairs of homologous chromosomes (2n = 4). During meiosis I, each pair of homologous chromosomes can align in two different ways on the metaphase plate.
   • This results in $2^n$ possible combinations of chromosomes in the gametes, where $n$ is the number of chromosome pairs. For our example with two pairs, $2^2 = 4$ different combinations are possible.

4. Verify and Summarize:

   • The four possible combinations of chromosomes ensure that each gamete is genetically unique. This genetic diversity is crucial for evolution and adaptation.

Final Answer

Yes, random assortment during a single meiosis can create four different genetically unique gametes, assuming there are two pairs of homologous chromosomes. This is due to the independent assortment of chromosomes, which results in $2^n$ combinations, where $n$ is the number of chromosome pairs.