<p>Here the key excerpts from the article: </p>
<p>1) They don’t, however, represent the true odds of a well-qualified student’s being admitted to a top school.</p>
<p>2) top students have been sending out more applications.</p>
<p>3) But while the best students are sending out more applications for the same number of slots at elite colleges, the slots themselves aren’t becoming more scarce and the number of students competing with one another isn’t growing.</p>
<p>4)It’s the percentage of top students who are admitted to at least one top school. </p>
<p>5)Sure enough, 80 percent of top students were accepted to at least one elite school.</p>
<p>6) If you work hard and get good grades and test scores, there is very likely a place in the best schools for you.</p>
<p>The article can be summarized with a tautology: if you are a top student, you will get into an elite school. This is best seen in #3 where we are told that there is some sort of pigeonhole principle in the background: we have n-slots and n-students so the top n will map to the top n. The article also uses an equally weighted binomial assumption which doesn’t apply to this context…qualifications don’t create binomial sortings and colleges don’t use binomial decision points.</p>