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In a medical study patients are classified in 8 ways according to whether they have blood type \(A B^{+}\), \(A B \sim, A^{+}, A^{-}, B^{+}, B \sim, O^{+},\) or \(O^{-},\) 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.

If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet, how many points are there in the sample space?

A certain shoe conies in 5 different styles with each style available in 4 distinct colors. If the store wishes to display pairs of these shoes showing all of its various styles and colors, how many different pairs would the store have on display?

A California study concluded that by following 7 simple health rules a man's life can be extended by 11 years on the average and a woman's life by 7 years. These 7 rules are as follows: no smoking, regular exercise, use alcohol moderately, get, 7 to 8 hours of sleep, maintain proper weight, eat. breakfast, and do not eat between meals. In how many ways can a person adopt five of these rules to follow (a) If the person presently violates all 7 rules? (b) If the person never drinks and always eats breakfast?

A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer?

A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. How many different ways can a doctor prescribe the drug for a patient suffering from asthma?

In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?

If a multiple-choice test consists of 5 questions each with 4 possible answers of which only 1 is correct, (a) In how many different ways can a student check off one answer to each question? (b) In how many ways can a student check off one answer to each question and get all the answers wrong?

(a) How many distinct permutations can be made from the letters of the word columns? (b) How many of these permutations start with the letter \(m ?\)

A witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by 3 digits, the first of which is a 5 . If the witness cannot recall the last 2 digits, but is certain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check