4. Ajury pool consists of 9 men and 11 women. Thejury will be made up of 12 jurors. a. f 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 court officer chosen to draw the names is a man? b. ow many ways can the jury be formed if there are no restrictions on composition? c. ow many ways can 8 women be chosen? d. ow many ways can 4 men be chosen? e. What is the probability that the random selection ofthe jury will result in 8 women and 4 men? 5. 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 city 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? ow many ways can 3 Republicans be chosen? ow many ways can 2 Democrats be chosen? e. What is the probability that the random selection of the fiveperson committee will result in 3 Republicans and 2 Democrats? E" F'- 6. An engineering company has four openings and the applicant pool consists of six database administrators and eight network engineers. All are equally qualified so the hiring will be done randomly. The hiring committee consists oft-1r women and 4 men. a. fone person on the hiring committee 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. ow many ways can the group who are to be hired be formed if there are no restrictions on composition? c. ow many ways can 3 database administrators be chosen? d. ow many ways can 1 network engineers be chosen? e. What is the probability that the random selection of the four persons to be hired will result in 3 database administrators and 1 network engineer? 7. A stJdentfaculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. a. f one person from the group of volunteers is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a student? b. ow many ways can the committee of four be formed if there are no restrictions on composition. c. How many ways can two of the students be chosen? d. ow many ways can 2 faculty be chosen? e. What is the probability that the random selection of the fourperson committee will result in two students and two faculty