Final answer:
A male Drosophila melanogaster can produce 16 genetically different kinds of sperm calculated by the principle of independent assortment during meiosis, which yields 2 to the power of the number of chromosome pairs (2^4 = 16).
Step-by-step explanation:
Drosophila melanogaster, commonly known as the fruit fly, has four pairs of chromosomes, resulting in 24 or 16 possible combinations of chromosomes that can be produced during gamete formation. This estimation comes from the principle of independent assortment, which applies during meiosis. However, the student's question specifies that crossing over does not occur in the formation of sperm in Drosophila melanogaster. Therefore, without crossing over, the number of genetically distinct kinds of sperm that can be produced is purely based on independent assortment of the chromosomes.
The random orientation of each of the four pairs of homologous chromosomes during metaphase I of meiosis I can lead to 2n different combinations of chromosomal assortments, where n is the number of chromosome pairs. For Drosophila melanogaster, which has n = 4, this would yield 24 or 16 possible combinations. Hence, a male Drosophila melanogaster has the potential to produce 16 genetically different kinds of sperm when considering independent assortment alone.