What are the $2^{23}$ combinations in gamete fusion?

Question

According to my textbook, when two human gametes fuse, there's $2^{23}$ different combinations of chromosomes, but I don't see how that is. The chromosomes are homologous, so they don't have any choice to make, and if they did have a choice to make, there'd be a different formula. Are there two oocytes perhaps, and each chromosome in the sperm can chose either one of the homologous chromosomes that exists in the respective oocytes, a choice available to each of the 23 chromosomes, thus yielding $2^{23}$ possibilities?

EDIT:

My textbook made the above claim as a sidenote to its explanation of meiosis. See my translated quotation under (bold made by me):

Therefore, four possible gametes can be formed (BR, Br, bR and br). If we take all 23 chromosome pairs into account, it will be almost 8.4 million ($2^{23}$) combination possibilities. And when two gametes are finally to fuse, the number of combination possibilities increase to almost 70 000 billion ($2^{23} \cdot 2^{23}$).

As you can see, my textbook says the fusion of gametes can happen with $2^{23}$ different combinations of chromosomes. Since I think I've read somewhere that the (pre?)fetus is triploid at some point, it makes sense to me that these combinations come from the fact that each chromosome from the sperm can pick a homolog from either of the two homologs available from the two oocytes. That's $2^{23}$ possibilities (assuming the sperm comes with only Xs).

My textbook is Naturfag Påbygging, by Aschehoug.

Answer 1

The calculation is actually quite simple. Each gamete can contribute one of two sister chromatids for each chromosome, so that in humans (with 23 distinct chromosomes) the number of possible combinations in the progeny cell resulting from fusion of the male and female gametes is:

4²³ (aka approx. 64 trillion — actually approx 70 trillion)

The number 2²³ (aka approx. 8 million — hence the erroneous 64 trillion in the source cited below), much loved by various sources including the poster’s text book, is the number of possible combinations of sister chromatids for each individual male or female gamete before fusion.

This is explained with illustration in Biolibre texts in the section entitled “Independent Assortment and Random Fertilization”.

I have no idea why there is an obsession with the number of pre-fusion combinations when the interest of the reader is surely the number of possible outcomes. As a non-biologist the difficulty for me in understanding the explanations I have read is the way that the genetics and cell biology are dealt with together. I admit that the cell biology is important, but if I had to lecture on this topic I would do the genetics first, and then the cell biology.

This explanation is hinted at in the comment from @BryanKrause, but I think that the textbook is at fault, and the poster’s confusion is justified.

Answer 2

Shouldn't it be that there are 2^23 different types of gametes possible from a single individual with 23 chromosomes? The math behind it is as follows:

Case 1: Only one chromosome. Let's say, from the diploid precursor with 2 homologs of chromosome 1. Half of the gametes would be with the 1A homolog, the other half with the 1b homolog. So, 2^1 types of gametes.

Further cases: More chromosomes. Consider two chromosomes, 1 and 2, each with 2 homologs (1A, 1B and 2A, 2B). Because each chromosome assorts independent of every other, 2^2 (= 4) possible combinations are possible. 1A-2A, 1A-2B, 1B-2A, and 1B-2B.

Extending the math, this would amount to 2^23 combinations for 23 chromosomes, leading to these many (~8.3 million) gametes from a single human. Each of these haploid gametes from a male, would combine with a gamete from a female. In each successful fertilization event, the resulting cell would have 46 chromosomes, restoring the diploidy.

I think your textbooks arrives at the 2^23⋅2^23 (= 70,000 billion) by taking into account all the combinations. Since each of the 2^23 male gametes can combine with each of the 2^23 female gametes, the overall combinations come out to be just that. I don't know where you got that fetus is ever triploid (will be happy if you share the source). I still cannot relate this to two oocytes. I'm saying this because your textbook also doesn't mention anything about 2 oocytes (I'm assuming). It just states a combinatorial fact.