<p>I am sure you are the first to have done this. I also don’t think they would hold it against you for applying to Dartmouth and 10+ other schools. Just email admission to let them know it was a mistake.</p>
<p>Of course if your friend wrote, “I know Dartmouth is my friend’s first choice and he has dreamed of going Dartmouth since he was 5,” then it maybe more of a problem.</p>