You cannot multiply admission rates because the admissions decisions are not random, however much they might sometimes seem so. If they each had a 10% admission rate, it’s not (0.1)^8 chance of a particular applicant getting into all of them. They are not unrelated events.
Put it this way: the applications are not randomly drawn from a hat. They are carefully and extensively scrutinized. If you get in to more than one school, it’s probably because, after getting past the academic basics of having high grades and test scores, the rest of your application contained compelling and distinctive information about what makes you uniquely exceptional. Each school (ivy) that accepts you does so for pretty much the same reason, they read your application and it strikes them that they’d much rather have you than most of their applicants.
Imagine 10 applicants represented by cars: 4 old (but running) Corollas, 3 recent model year Accords, a new Miata, a new Mustang, a new Outback, and a 1966 Ferrarri in pristine condition. Now imagine 8 Ivy schools represented by car buyers; they are told they can make offers on 2 of the cars, and there is no real difference in price. Every single one will make an offer on the Ferrarri, and probably an offer on one of the Miata, Mustang, or Outback because they know that everyone else will make an offer on the Ferrarri and they can’t all get it.
The kid who gets the admission offer to all 8 Ivies is the Ferrarri. (Or at least, his application is.) Everyone wants him, for the same reasons. There is nothing random about it.