2.22. In a medical study patients are classified in 8 ways according to blood types AB+, AB-, A+, A-, B+, B-, O+, O- and also according to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.

2.47. A college plays 12 football games during a season. In how many ways can the team en the season with 7 win, 3 losses, and 2 ties?

2.65. In a high school graduating class of 100 students, 54 studied mathematics, 69 history and 35 both mathematics and history. If one of these students is selected at random, find the probability that

a) the student took mathematics or history;

b) the student did not take either of these subjects;

c) the student took history but not mathematics.

2.96. The probability that a person visiting his dentist will have an X-ray is 0.6; the probability that a person who has an X-ray will also have a cavity filled is 0.3; and the probability that a person who has had an X-ray and a cavity filled will also have a tooth extracted is 0.1. What is the probability that a person visiting his densist will have an X-ray, a cavity filled, and a tooth extracted?