2.Registrants at a large convention are offered 6 sightseeing tours on each of 5 days. In how many ways can a person arrange to go on a sightseeing tour planned by this convention?

3.How many ways are there to select 4 candidates from 9 equally qualified recent graduates for openings in an accounting firm?

4.Four married couples have bought 8 seats in the same row for a concert. In how many ways can they be seated if each couple is to sit together?

5.How many 5 - letter ordered codes can be formed with letters A, B, C, and D if we allow repeated use of the letter?

6.In how many ways can a true-false test consisting of 9 questions be answered?

7.Students at a private liberal arts college are classified as being freshmen, sophomores, juniors, or seniors, and according to whether they are male or female. Find the total number of possible classifications for the students at that college.

8.Carla is going to arrange her 4 books on a shelf: Algebra, Trigonometry, Geometry, and Calculus. How many different possible arrangements can she make?

9.If 3 specific persons, among 6, insist on following each other, how many ways are possible?

10.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 ways can a doctor prescribe the drug for a patient suffering from asthma if there are no restrictions if the doctor patronizes a certain manufacturer?

11.How many distinct permutations can be made from the letters of the word COLUMNS?

12.How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 5, and 6 if each digit can be used only once?

13.How many four - digit odd numbers can be formed from the digits 0, 1, 2, 3, 5, and 6 if each digit can be used only once?

14.If 3 specific persons, among 6, refuse to follow each other, how many ways are possible?

15.In how many ways can a window dresser display four shirts in a circular arrangement?

16.If you are given the word "PARALLEL", compute the number different 8 - letter arrangements can be formed.

17.If a multiple-choice test consists of 5 questions, each with 4 possible answers of which 2 is correct, in how many ways can a student check off one answer to each question and get all the answers wrong?

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

19.If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, in how many ways can a student check off one answer to each question?

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

21.A standard deck of cards has 52 different cards. How many 3 card order arrangements can be made by selecting 3 cards without replacement?

22.Find the number of permutations of 5 objects with one object repeated 3 times and a second object repeated 2 times.

23.In how many ways can 6 people be lined up to get on a bus?

24.In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate?

25.A certain brand of shoes comes in 4 different styles, with each style available in 4 distinct colors. If the store wishes to display pairs of these shoes showing all its various styles and color, how many different pairs will the store have on display?

26.A standard deck of cards has 52 different cards. How many 3 - card order arrangements can be made by selecting 3 cards with replacement?

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

28.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 screened porch. How many different plans are available to this buyer?

29.You know that the extension of a private telephone is 272 but you have forgotten the last 4 digits. You can only recall that the last 4 digits are 3, 6, 8, and 9 but you do not know the order. What is the maximum number of telephone calls you will need to make to dial the correct number?

30.How many four - digit numbers can be formed from the digits 0, 1, 2, 3, 5, and 6 considering it to be greater than 3300 if each digit can be used only once?

31.Find the number of permutations of 7 objects with one object repeated 4 times.

32.In how many 3 oaks, 4 pines, and 2 maples be arranged along a property line if one does not distinguish among trees of the same kind?

33.A California study concluded that following 7 simple health rules can extend a man's life by 11 years on average and a woman's life by 7 years. These 7 rules are as follows: no smoking, get regular exercise, use alcohol only in moderation, 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 4 of these rules to follow if the person presently violates all 7 rules?

34.How many distinct permutations can be made from the letters of the word "INFINITY"?

35.A California study concluded that following 7 simple health rules can extend a man's life by 11 years on average and a woman's life by 7 years. These 7 rules are as follows: no smoking, get regular exercise, use alcohol only in moderation, 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 4 of these rules to follow if the person never drinks alcohol and always eats breakfast?

36.A drug for the relief of asthma can be purchased from 5 different manufacturers in tablet or capsule form, all of which come in regular and extra strength. How many ways can a doctor prescribe the drug for a patient suffering from asthma if there are no restrictions?

37.In how many ways can a caravan of 8 covered wagons from Arizona be arranged in a circle?

38.A contractor wishes to build 7 houses, each different in design. In how many ways can he place these houses on the street if 4 lots are on one side of the street and 3 lots are on the opposite side?

39.In how many ways can 7 different trees be planted in a circle?

40.Four married couples have bought 8 seats in the same row for a concert. In how many ways can they be seated if all men sit together to the right of all the women?

41.How many of these permutations start with the letter M of the word COLUMNS?