Points) During June, Colleen’s Motors sold 75 cars with heated seats, 95 with GPS, and 100 with a sunroof. Twenty cars had all three options. 10 cars had none of these options, and 10 cars were sold that had only heated seats. In addition, 50 cars had both a sunroof and a GPS, and 60 cars had both a sunroof and heated seats. a. How many cars were sold in June? b. How many cars had only a GPS? 2. (6 points) In how many ways can you choose two groups of three people from among eight people? 3. (6 points) A meeting is to be addressed by 5 speakers, A, B, C, D, and E. In how many ways can the speakers be ordered if B is to speak immediately after A? 4. (10 points) An admission test is given by a university contains 10 true-false questions. Eight or more of the questions must be answered correctly in order to be admitted. a. How many different ways can the answer sheet be filled out? b. How many different ways can the answer sheet be filled out so that 8 or more questions are answered correctly? 5. (8 points) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 apples? 6. (8 points) Expand ( + 6)2 using the Binomial Theorem. 7. (10 points) There are 25 quarts of milk on a supermarket shelf, 6 of which are spoiled. A customer buys three quarts of milk. a. How many samples contain exactly 3 quarts of spoiled milk? b. How many samples contain at most 2 quarts of spoiled milk? 1 Pace University MAT104 CRN 20537 S. Lin Spring 2020 Exam 2 April 1, 2020 8. (10 points) Let and be two mutually exclusive events of a sample space S. If () = 0.6 and () = 0.2, find each of the following probabilities: a. (∩) b. (′) c. (∪) d. (′) 9. (8 points) A lottery game has balls numbered 1 through 11. If a ball is selected at random, what is the probability of obtaining an odd numbered ball or the number 11 ball? 10. (8 points) What is the probability that seven-digit phone number has one or more repeated digits (leading digit cannot be zero)? 11. (8 points) A