A mathematics and another question

[Sporting]

I didn't know until yesterday that Emma Raducanu has a Chinese mum and a Romanian dad (though the surname is a big clue!). Anyway, given that there are 195 countries in the world (depending on definition) how many different inter-country combinations are possible?

Also, I wonder what's the most common international romantic relationship. Canada- USA? And which would seem the most unlikely for whatever reason, whether due to population size, geography or political considerations?

[ad hoc]

The first one would be 195+194+193+...+1

But I can't be bothered to work that out

[ad hoc]

Actually no, sorry, the sequence would start with 194

[Sporting]

Isn't Janik good at these things?

[Nefertiti2]

I believe its 18915
195*194 /2

but someone else may know better.

[ursus arctos]

The assumption that individuals are of a single nationality (let alone a single ethnicity) strikes me as fundamentally flawed.

That said, 195 factorial for the first question and Vatican City-Nauru for the second (the Vatican has both the smallest population of any sovereign and the most skewed sex ratio). Nauru is third smallest, but is much further from the Vatican (in every respect) than Monaco (which is second).

[Sporting]

The assumption that individuals are of a single nationality (let alone a single ethnicity) strikes me as fundamentally flawed.

Of course. But otherwise the question takes on almost impossible permutations.

[Sporting]

That said, 195 factorial for the first question and Vatican City-Nauru for the second (the Vatican has both the smallest population of any sovereign and the most skewed sex ratio). Nauru is third smallest, but is much further from the Vatican (in every respect) than Monaco (which is second).

The skewed sex ratio shouldn't count for bare stats purposes, though obviously real-life considerations come into play.

[ursus arctos]

You appear to be asking a question about a world that does not exist

[Sporting]

True. All a result of last night's insomnia and an over-productive mind.

[ad hoc]

Most common percentage-of-population wise will probably be two countries that were one within living memory (eg Czechia-Slovakia, Serbia-Croatia), but numbers would point more to somewhere like Russia-Ukraine. (It may well be that based on numbers alone the most common relationship is India - China)

[ad hoc]

Plus I think ursus is wrong with 195 factorial, which is 195*194*193...*2 . That's way too high

[Balderdasha]

I mean, in the real world this is obviously nonsense, as it wouldn't include my own British / Italian / Palestinian children. And wouldn't have included any children I'd have had with my previous boyfriend who would have been potentially eligible for UK / USA / HK nationality.

But leaving that aside, ursus' calculation is essentially correct. 195 factorial is 18,915, but I think the answer is 18,914 for all two country combinations. If you include people with both parents having the same nationality, there are 19,109 possibilities. I checked ursus' methodology via Google and I even went through and did 194+193+192+191 etc manually.

[Balderdasha]

Emma Raducanu was also born in Canada to add to her international heritage.

[Janik]

The first one would be 195+194+193+...+1

But I can't be bothered to work that out

Actually no, sorry, the sequence would start with 194

There is no need to calculate an arithmetic sequence like this longhand. The numbers pair up - 1 + 194 = 195; 2 + 193 = 195; 3 + 192 = 195; etc. That gives a simple formula for calculating the total, which is s = n * ((a(1) + a(n))/2)
n = the number of terms, 194 in this case
a(1) = the first term of the sequence (1 for us)
a(n) = the nth term (194 here)

So in our particular example the numbers to punch in to the calculator are 194 * 97.5 = 18915

[ursus arctos]

Plus I think ursus is wrong with 195 factorial, which is 195*194*193...*2 . That's way too high

You are correct

[ursus arctos]

For most common in terms of percentage, I would also look at microstates with large neighbours: Vatican/Italy, San Marino/Italy,Monaco/France, Andorra/Spain, etc

[Rogin the Armchair fan]

I don't think the Vatican City is included on country lists that require UN membership (on the basis that it isn't). For least likely international couplings, certainly in recent years, North Korea sprang to mind.

[Janik]

195 factorial is 18,915

No, it isn’t. Ad hoc is right on this 195! is an enormous number as it equals 195 * 194 * 193 etc. Factorials are geometric sequences, not arithmetic ones. 195 * 194 alone = 37830 (10! = 3628800 to give an example of how ridiculously fast factorials grow)

What you want here is a statistical calculation called a combination. See here for an explanation: https://www.britannica.com/science/permutation

I will leave it to someone else to push 195! / (193! * 2!) through a calculator. But that will be your answer to how many pairs are possible, including the one of the same country.

[ursus arctos]

The idea that Switzerland was not a "country" before 2002 (or that "countries" didn't exist before 1945) is rather risible

[Janik]

! is mathematical shorthand for factorial, btw. In case anyone hadn’t got that. So 5! = 5 * 4 * 3 * 2 * 1 (= 120, for the record). Etc.

[ursus arctos]

Janik, is there a name for the arithmetic sequence that I have forgotten/never learned?

[ad hoc]

I used to love the other name for factorial, given its notation = "shriek" (So five shriek is 120)

[ad hoc]

The idea that Switzerland was not a "country" before 2002 (or that "countries" didn't exist before 1945) is rather risible

What's this in reference to?

[Janik]

Actually, no need, it’s 18915 as already calculated, isn’t it. The combination collapses to the arithmetic sequence when only unordered pairs are needed.