It has been estimated that one in five Americans suffers from allergies. The president of Hargrove University plans to randomly select 10 students from the undergraduate population of 1400 to attend a dinner at his home.
Assuming that Hargrove students are typical in terms of susceptibility to allergies and that the college president's home happens to contain just about every common allergen to which afflicted persons react, what is the probability that at least 8 of the students will be able to stay for the duration of the dinner event?