The first thing that comes to mind is that you will get more useful responses on this web site if you give us more useful information to go with. As one example, I do not see the name of the university where your daughter was rejected. I see it described as “P”, which makes me think of Princeton, except that Princeton does not have early decision (they do have SCEA – single choice early action). I will assume for the purpose of this post that it was either Princeton, or a similarly highly ranked university or college.
Rejection from Princeton is the most likely outcome for even very strong students. Assuming that she does not literally have a Nobel Prize, and that neither parent is the head of state of a medium sized country, rejection is the most likely outcome by far even for the strongest students. I have seen estimates for other top schools (specifically Stanford and MIT) that somewhere around about 80% or 85% of applicants are academically qualified to attend, but closer to 4% or maybe 5% get accepted.
Also, admissions at the most selective (also known as “rejective”) universities in the US is very hard to predict, and is not entirely based on merit. You can neither accurately predict nor count on getting accepted to any of the top 10 or even top 20 universities.
However, as many of us have said many times, there are a huge number of very good universities in the US. You can get a great education at any one of at least 200 colleges and universities in the US or at any one of just as many schools outside the US. There are very good research and internship opportunities at hundreds of different schools. At least in my family we have lots of experience that supports this.
Another piece of advice that I can suggest is that the student should be authentic. They should participate in the ECs that are correct for them. They should take the classes that are correct for them. Their essays should come from the student themselves and reflect the student’s own feelings and thoughts. I did not even read my daughter’s essays. I trusted them to do a good job.
You might want to read the “applying sideways” blog on the MIT admissions web site. As I understand it, it recommends that the student take the classes that are right for them, participate in the ECs that are right for them, be kind, be authentic, and whatever you do, do it well. This is pretty much exactly what I did to get into MIT (for a bachelor’s degree) and Stanford (for a master’s degree). This is what my wife did to get into Columbia (master’s), and what our daughters did to get into very good graduate programs that are a good fit for them (they are both currently studying for a doctorate, a DVM and a PhD). However the specific classes and ECs that each of us did were very different. What was right for me and what was right for my wife were not the same. Also, the four of us ended up at eight different universities (one each for a bachelor’s, and a different one each for graduate school). Again what was right for each of us was different.
When I was applying to graduate schools I was turned down by my “dream school” and instead attended my second choice. I eventually figured out that my second choice had always been a far better fit for me – I loved it. In the same sense, things usually work out very well for a wide range of academically strong students. Things just do not always work out exactly the same way that we had originally expected. If your daughter was turned down by her first choice, she is very likely to have a similar experience and get into another excellent university that turns out to be a good fit for her.
This whole system of university admissions in the US feels random, unpredictable, and unfair. However, it nonetheless works out very well for the large majority of academically strong students, with students ending up with admissions to very good universities that are a good fit.
Best wishes. I expect that this will work out well one way or another.