3) Each year a college awards five merit scholarships to entering freshmen with exceptional high school records. The initial pool of applicants has been reduced to a "short list" of 8 men and 10...

Extracted text: 3) Each year a college awards five merit scholarships to entering freshmen with exceptional high school records. The initial pool of applicants has been reduced to a "short list" of 8 men and 10 women, all of whom seem equally deserving. If the awards are going to be made at random from the short list, what is the probability that both men and women will receive scholarship offers?