1. A total of twelve hundred graduates of State Tech have gotten into medical school in the past several years. Of that number, one thousand earned scores of twenty-seven or higher on the MCAT and four hundred had GPAs that were 3.5 or higher. Moreover, three hundred had MCATs that were twenty-seven or higher and GPAs that were 3.5 or higher. a) Illustrate the given situation using a Venn diagram b) What proportion of those twelve hundred graduates got into medical school with an MCAT lower than twenty-seven and a GPA below 3.5?

c) What proportion of those twelve hundred graduates got into medical school with an MCAT scores of twenty-seven or higher only?

2. A vice president and a secretary are to be chosen from an organization consisting of 30 people. How many different choices of officers are possible if a) there are no restrictions; b) Alice will serve only if she is the vice president; c) Bob and Cath will serve together or not at all; d) Divine and Ethel will not serve together?