Until you've been through it, it's hard to appreciate just how elusive a top Ivy school is.
Take a look at this breakdown of Princeton's incoming Class of 2020:
https://www.princeton.edu/main/news/archive/S45/94/44G37/index.xml?section=topstories
1,894 kids accepted
Half are Male, now there are only 947 slots left
Half are people of color, now there are only 474 slots left
11% are alumni kids, if two-thirds of those are white (and so not previously counted as people of color), now there are 440 slots left
17% are first in their family to attend college, if one-third of those are white (and so not previously counted), now there are 415 slots left
Princeton admits about 200 recruited athletes per year. Half are female (because of Title IX) and if half of those are neither people of color nor first-generation students, now there are 365 slots left.
Whoops, almost forgot. 11.7% of the class are international students, which the federal government doesn't allow colleges to include in their under-represented minority reporting. Now we're down to 322.
That's it. By a conservative estimate, Princeton has about 322 slots for every white, non-legacy, non-recruited athlete daughter of college-educated parents in the entire country. And that's without counting VIP/celebrity kids, extremely wealthy kids, faculty kids, etc.
Is your DD one of those top 322 applicants?