Haven't really browsed /sci/ before but I have a math question and it has been bugging me. So to start we all know about rare diseases and the chance of getting one for example it could be every 1 in 500 gets X disease.

So my question is for a super rare disease like HGPS(https://americanpregnancy.org/healthy-pregnancy/birth-defects/progeria-704/) every 1 in 4-8 million what are the chances of multiple(say 3-6) people being born with it in short succession, or if that is too broad then then span of one day given that there are only about 380,000+ babies born each day?