The 700-room Westin Charlotte offers a premiere uptown location in the heart of the city’s financial district. On a busy weekend, the hotel has 20 rooms that are not occupied. Suppose that smoking is allowed in 8 of the rooms. A small tour group arrives, which has four smokers and six nonsmokers. The desk clerk randomly selects 10 rooms and gives the keys to the tour guide to distribute to the travelers.
a. Compute the probability that the tour guide will have the correct mix of rooms so that all members of the tour group will receive a room that accommodates their smoking preferences.
b. Determine the probability that the tour guide will have to assign at least one nonsmoker to a smoking room.