On a busy weekend, a hotel has 20 rooms that are not occupied. Suppose that smoking is allowed in 8 of the rooms. A small tour group arrives that 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 assign at least one nonsmoker to a smoking room.