Re: Verification required for maths-tard.
Let me show my working, just like in maths exams all those years ago when I was in school.
Do it for a population of N people, and then set N equal to 60 million.
Imagine N people. Each one could be paired with any of the N-1 others. So, for each person, that's N-1 pairs. And since there are N people altogether, that's N*(N-1) pairs.
But these are ordered pairs. We're pairing Alice with Bob, (A, B), and also pairing Bob with Alice, (B, A). We're counting those as two pairs, when they're really the same pair reversed. So we need to discount all these duplicates. And since each pair will be effectively counted twice (once when pairing Alice with everyone else, (A, x), and once when pairing everyone else with Alice, (x, A), for example), that means we just need to halve the total. That gives us a total of N*(N-1)/2 distinct, unordered pairs.
Or, counting it a different way, we can take the first of the N people, and pair them up with the N-1 others, producing N-1 pairs. Then, we can take the next person, and pair them up with the remaining N-2. The third gets paired up with the N-3 that are left. In total, we end up with N-1 + N-2 + N-3 + ... + 3 + 2 + 1 pairs. It turns out to be N*(N-1)/2 pairs altogether.
Either way, for N people, there are N*(N-1)/2 distinct pairs.
Try it with N=4, for Alice, Bob, Carol and Dave. You'll end up with six pairs (not including reversed duplicates). That's 4*(4-1)/2 = 4*3/2 = 12/2 = 6.
And here are those pairs: (A, B), (A, C), (A, D), (B, C), (B, D), (C, D).
Now set N to 60 million. That then gives 60,000,000*(60,000,000-1)/2
= 30,000,000*(60,000,000-1)
= 30,000,000*60,000,000 - 30,000,000
= 1,800,000,000,000,000 - 30,000,000
= 1,799,999,970,000,000 pairs.
It is sometimes said that only one in a billion pairs of people would have the same DNA profile. So, divide the total number of pairs by one billion, 1,000,000,000, and that's the number of pairs that would be such pairs of people with the same DNA profiles as each other.
For N=60,000,000, that's 1,799,999.97 pairs of people with the same DNA profiles. Or just three hundredths of a pair less than 1.8 million. Roughly.
Now do it for the EU, with a population of about half a billion. You end up with about 125 million pairs with the same DNA profiles. That's going to include more people than in the whole of the UK population, and a sizeable chunk of the EU's population.
And now do it for the global population of over six billion. If N=6,000,000,000, we get something like 18 billion pairs - more than the number of people in the world! That means the average person (for a suitable definition of the term "average") would be in more than one such pair. You are likely to have the same DNA profile as at least a few other people on this planet.
Feel free to copy and paste this working-out if you find that helpful.