More than 12,000 students applied for admission to Notre Dame this year, surpassing by 19 percent the record set three years ago. Daniel Saracino, assistant provost for enrollment, attributed the increase to several factors: increased availability of financial aid, stepped up visits by admissions officers to high schools, more students and high school counselors visiting campus, expanded summer programs on campus for high school students, and the positive image projected by first-year football coach Tyrone Willingham, the first black head coach in any sport at Notre Dame. Perhaps due to publicity about Willingham, applications from minority students rose about 45 percent this year. Students of color have accounted for about 17 percent of Notre Dame’s student body in recent years. Next fall they might reach 20 percent for the first time, Saracino said. The University admits about 3,200 applicants and expects about 1,960 to accept and enroll. Decision letters were to be mailed by April 1. Notre Dame, Harvard, Yale, Princeton, Stanford, Dartmouth, Brown, MIT and Rice are the only universities that admit fewer than half of all applicants and have more than half of those admitted choose to enroll.