1. Sleeping arrangements. Your family is trying to decide sleeping arrangements in the house. There are 10 young people staying in the house who will be divided into two rooms. You will choose a set of 5 people to sleep in the rst room and the rest will sleep in the second room. A sleeping arrangement is acceptable if it meets the following two criteria: 0 Your two youngest cousins (say, 7 and 8 years old) always ght, so exactly one of them must be in the rst room. 0 There are 4 people over 18 years old, and exactly 2 of them must be in the rst room to supervise the others. You are too lazy to work out the arrangement by hand, so you decide to do this randomly by choosing a set of 5 people at random to sleep in the rst room, and repeat this until you get an acceptable arrangement. (a) (4 pts) For a single draw of 5 people, what is the probability that you will draw an acceptable sleeping arrangement? (b) (6 pts) What is the expected number of draws of 5 people until you get an acceptable arrangement? Note: Each drawing of 5 people is independent of every other drawing of 5 people