8. The executives in a company are four women and three men. Three are to be chosen at random to attend a management seminar. a. If one person from the executives is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a woman? b. How many ways can the group of attendees be formed if there are no restrictions on composition? C- How many ways can one man be chosen? d. How many ways can 2 women be chosen? e. What is the probability that the random selection of the three-person group will result in two women and one man 9. In a class of 18 students there are 11 math majors and 7 computer science majors. Four students are randomly picked to prepare a demonstrate on the use of a graphing calculator. a. If one person in the class is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a math major? b. How many ways can the group of students be formed if there are no restrictions on composition? How many ways can three math majors be chosen? d. How many ways can 1 computer science major be chosen? What is the probability that the random selection of the four-person group will result in three math majors and 1 computer science major? 10. A jury pool consists of 9 men and 11 women. The jury will be made up of 12 jurors. a. If one person from among 6 court officers (3 women and 3 men) is chosen at random from to draw the names out of a hat, what is the probability that the person chosen to draw the names is a man? b. How many ways can the jury be formed if there are no restrictions on composition? C- How many ways can 8 women be chosen? d. How many ways can 4 men be chosen? e. What is the probability that the random selection of the jury will result in 8 women and 4 men? 11. A city council consists of ten members. Four are Democrats and six are Republicans. A committee of five to study transportation issues will be randomly selected. a. If one person on the council is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a Democrat? b. How many ways can the committee be formed if there are no restrictions on composition? C- How many ways can 3 Republicans be chosen? d. How many ways can 2 Democrats be chosen? e. What is the probability that the random selection of the five-person committee will result in 3 Republicans and 2 Democrats