Question

An organism has 6 chromosomes (2n = 6) or 3 pairs of homologous chromosomes. Assuming no crossing over occurs, how many different combinations of maternal and paternal chromosomes would be possible in its gametes? Remember that each gamete will contain three chromosomes, and each of these will be either maternal or paternal. (Denote maternal chromosomes M1, M2, M3 and paternal chromosomes P1, P2, P3.) List the possible eight combinations. (Remember the formula is 2n, so in this case 23 = 8.)

Answer 1

M1, M2, M3
P1, P2, P3
3 types each of 2 groups
$= {2}^{n} \: where \: n = number \: of \\ chromosomes \: each \\ {2}^{n} = {2}^{3} = 8$

1) M1, P2, P3
2) M1, P2, M3
3) M1, M2, P3
4) M1, M2, M3
5) P1, P2, P3
6) P1, M2, P3
7) P1, P2, M3
8) P1, M2, M3

Answer 2

The formula 2ⁿ is usefull to get the number of gametes that results from the independent segregation of alleles. All the possible gametes are M1M2M3 / M1P2M3 / M1M2P3 / M1P2P3 / P1M2M3 / P1P2M3 / P1M2P3 / P1P2P3.

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Following the statement of the problem, the way to know how many different gametes can be formed, is applying the formula 2ⁿ. So let us analyze it.

• Gamete formation involves the random and independent segregation of the alleles.

• During anaphase I (meiosis) occurs the independent separation of homologous chromosomes that migrate to opposite cell poles.

• This separation generates different chromosomal combinations in the daughter cells.

• There are two alternatives per homologous pair.

The number of gametes with different combinations is 2ⁿ, where  

n = number of homologous pairs.  

In the exposed example,

• The number of homologous pairs is n = 3

• Number of gametes = 2ⁿ = 2 ³ = 8

We know that

• maternal chromosomes M1, M2, M3

• paternal chromosomes P1, P2, P3

Then, in the diploid cell is  M1P1  M2P2  M3P3.

Gametes are haploid cells formed by the combination of chromosomes, so

1. M1 M2 M3
2. M1 P2 M3
3. M1 M2 P3
4. M1 P2 P3
5. P1 M2 M3
6. P1 P2 M3
7. P1 M2 P3
8. P1 P2 P3

If it results easier for you, you can make a diagram like the one in the attached files.

     

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