Question

a set of dizygotic twins share mother's womb and are born together but do not share same genes. How is it possible?

Answer 1

To understand you have to concentrate on the word dizygotic, and also on the fact that each gamete is genotypically unique due to crossing over that takes place during meiosis; also due to the fact that there is independent assortment.

Explanation:

Point 1.

An embryo develops from a zygote (=zygote is a single cell diploid entity produced after fertilisation between two haploid gametes, namely egg and sperm).

Dizygotic twins develop from two separate zygotes. This may happen when during ovulation, more than one egg is discharged in fallopian tube.

Two eggs could become fertilised by two different sperms and hence two genetically different embryoes will be formed in mother's reproductive tract. Dizygotic twins just share the womb, other wise they are like any other sibling.

Please read this answer about monozygotic and dizygotic twins.

Point 2.

Eggs are female gametes and sperms are male gametes. If the number of homologous pair in an organism is `n` then the number of different types of gametes is `2^n`.

That is if there are four pair of chromosomes in a cell of an organism, number of different gametes produced by the organism will be: `2^4` i.e. `16`. Then try to understand that in case of human the number is `2^23`, i.e. `8.5` million possibilities.

Moreover there is random fertilisation. Hence dizygotic twins can never have identical genotype, hence they are not clones. (Monozygotic twins are, because they start life as single zygote.)