I was wondering idly the other day how many possible different individuals two humans could produce.

Each parent contributes 13 chromosomes to a child, for 26 chromosomes overall.

But for each parent it's 13 non-repeating chromosomes out of 26, and it can't be any of the same chromosomes contributed by the other parent.

So I think the formula for number of possible unique children looks like this:

(Possible combinations of 13 unique chromosomes out of 26 from Parent A) x (possible combination of 13 unique chromosomes out of 26 from Parent B) - (any results that involve duplicate chromosomes from the parents)

So while I understand the basic math of combinations and permutations (13! is the number of possible combinations from 13 objects), this particular math problem outstrips my feeble remembrances from college.

Anyone able to lay out the math for me?

Or am I merely complicating the problem, and the actual answer is 26! -- or 4x10 to the 26th power -- the number of possible arrangements of 26 chromosomes?

If the latter, I'd still like to know how to figure out the "number of combinations of 13 nonrepeating objects out of 26 total objects".

__________________
Scarred survivor of the April 2008 Mod War.

Too early in the morning for me, raytri. Mark is coming home today. I'll try to remember to ask him. We used to do this kind of thing for fun (only much easier) when he was little. I think it would be helpful to use the alphabet. ABCD... for chromosomes from the MOM and abcd... for chromosomes from the Dad. AbCdEfGhIjKlMnOpQrStUvWxYz. Does that make sense?

__________________
Order without liberty and liberty without order are equally destructive. - Theodore Roosevelt

Consulting the genius! Yes!

Yes. The problem for me is the exclusivity. If was simply mixing two 13-letter combos, the answer (I think) would be 13! x 13!. What I don't know how to do is account for possible duplicates -- making sure there's not both a "B" and a "b". Plus how to figure out the number of 13-letter combos out of a group of 26 letters.

It probably involves something like n!/n!-b!, where n is the total number of objects and b! is the size of the subset I'm seeking to count.

__________________
Scarred survivor of the April 2008 Mod War.

OK - without looking anything up - I also think the answer is 26! - unless I'm missing something????

So are you suggestion that there are a finite set of humans born to the World? - but then there is the nature Vs nurture thing to complicate matters to make a World full of billions of wonderful individualists (except for me )

PS 26! = 4,032,914,611,266,056,355,840,000 - which is more than the Worlds population

Well, plus not every individual carries the same 26 chromosomes. Or rather they do, but the chromosomes have different genes attached.

I think 26! is even bigger than that: my calculator added two more zeros. In either case, it's a staggering number: two humans can produce far more distinct offspring in one generation than have ever existed on earth.

__________________
Scarred survivor of the April 2008 Mod War.

Isn't it 23 from each for a total of 46?

I think it might be a tad bit more complex than that -- remember that gametes are produced through meiosis, each representing a different combination of the the homologous pairs received by your mother and father. That is, each gamete (sperm or egg) has a unique genetic makeup of its own, pieced together from different parts of the parent chromosomes through process of "crossing-over." There is a mind-boggling degree of variation.

Ooops - yes I missed a "00" - yes a staggering number!!!

more that have ever existed on the earth throughout history - amazing really amazing!!!

I'd still like to figure out the math problem though.

Genes make the number even higher as far as how many different possible kids a couple could have. Even then, you'd have to take into account dominant genes. For instance, of all the Asian/white couples I know, the kids always have Asian physical features.

Y'all decide whether to go with the math problem or the gene problem. I got a genius for either question. The12thSon is the Biology Dept. nominee for THE most prestigious award given to graduating seniors at A&M. See how nicely I worked that in?

__________________
Order without liberty and liberty without order are equally destructive. - Theodore Roosevelt

Oh, you're thinking of *Earth* humans....

Oops. See what happens when I don't look stuff up?

Let me make sure I understand this. A single chromosome in a gamete might include pieces taken from more than one chromosome of the parent? And then those pieces are mixed together with the gamete from the other parent? Meaning that it's not chromosomes, but parts of chromosomes that are being inherited? So my X chromosome, for example, might contain genes from both parents?

__________________
Scarred survivor of the April 2008 Mod War.

When I think of permutations I think of sequences, like pulling cards from a deck. To calculate the number of possible different combinations of genes, wouldn't you just use 2^23 given two options "A" or "a" across 23 chromosomes?

e.g. if we had a three chromosome organism, the number of possible unique gametes (not considering mutations or crossing over) would be 2^3 (8 ) not 3! (6):
Combining ABC and abc we get:
ABC, ABc, AbC, aBC, Abc, ABc, aBC, abc

Thus, for 23 chromosomes, the number of unique gametes would be 2^23 or 8,388,608.

Combining one gamete from each parent results in 8,388,608 x 8,388,608 or 70,368,744,177,664 different combinations.