1. i will be sharing an apartment with two friends. The apart¬ment has one large and one small bedroom. Two of us will
share the large bedroom and the other will sleep in the smaller mom.
(a) In how many distinguishable ways can we assign moms?
(b) What is the probability that I get the single room, if we choose randomly
2.Suppose that a movie theater places seven distinct positive integers not exceeding 60 on each movie ticket in no partic-ular order. On the day you buy a ticket, the movie theater randomly selects seven distinct positive integers not exceed¬ing 60 and awards a free movie to any person with a ticket containing all seven of these numbers. You receive a ticket containing these seven numbers on it: 7. 15. 16. 27. 44. 45. 49.
(a) In how many ways can the movie theater select the seven distinct positive integers not exceeding 60?
(b) What is the probability that you will win a free movie?
(c) What is the probability that you will have at most one of the numbers correct?
3.Mom has seven jobs that she needs completed. The jobs are doing the laundry. mowing the lawn, vacuuming, washing the windows. folding the towels. cleaning the garage. and run-ning some errands. She will randomly assign you three of these jobs and will also assign a day on which each job must be completed. The jobs will be completed on Monday. Tues-day. and Wednesday. Assume that Mom will not ask you to do any job more than once in these three days.
(a) In how many ways can Mom assign the jobs for you to complete?
(b) what is the probability that you will have to fold the towels?