Problem Set 3 Part 2 These problems focus on counting techniques and probability. Related text: chapter 10 sections 10 - 1 examples 2, 3; 10 - 3 examples 3,4,5; 10 - 5 examples 1, 2, 4 Only do the one problem that corresponds to your assigned number. Be sure that you show all your work to reach your answer. Each step must be on a separate line. Your method to reach your answer must be clear and include explanations. For questions a and e, write the probability as a fraction reduced to lowest terms or as a decimal rounded to the nearest hundredth. For questions b, c, d the order of selection is not important so you use the combination rule not the permutation rule. 1. A student-faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. a. If 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. How 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. How many ways can 2 faculty be chosen? e. What is the probability that the random selection of the four-person committee will result in two students and two faculty?