The diploid number of a roundworm species is 4. Assuming there is no crossover, and random segregation of homologues during meiosis, how many different possible combinations of chromosomes might there be in the offspring (not including variety generated by crossing over)

16 possible combinations

Explanation:

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 poles of the cell. 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 there are 4 pairs of chromosomes, so

the number of possible combinations of chromosomes = 2ⁿ = 2⁴ = 16

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