Finite Math B, Chapter 8 Test Review Name Evaluate the factorial. 1) 6! A) 720 B) 120 C) 360 D) 1440 Evaluate the permutation. 2) P( 10, 5) A) 10 B) 30,240 C) 1 D) 720 3) P( 12, 8) A) 19,958,400 B) C) 495 D) 11,880 4) P( 25, 5) A) 6,375,600 B) 127,512,000 C) 303,600 D) 1.55 1025 Solve the problem. 5) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed? A) 900 three-digit numbers B) 1000 three-digit numbers C) 899 three-digit numbers D) 27 three-digit numbers 6) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed? A) 2401 four-digit numbers B) 840 four-digit numbers C) 23 four-digit numbers D) 24 four-digit numbers 7) License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? A) 308,915,776 plates B) 1,000,000 plates C) 1,757,600 plates D) 17,576,000 plates 8) A shirt company has 4 designs that can be made with short or long sleeves. There are 6 color patterns available. How many different types of shirts are available from this company? A) 10 types B) 24 types C) 48 types D) 12 types 9) A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 9 audio systems. How many ways are there to order this model of car? A) 172 ways B) 158 ways C) 170 ways D) 162 ways 10) A restaurant offers 7 possible appetizers, 13 possible main courses, and 6 possible desserts. How many different meals are possible at this restaurant? (Two meals are considered different unless all three courses are the same). A) 343 meals B) 546 meals C) 26 meals D) 536 meals
How many distinguishable permutations of letters are possible in the word? 11) CRITICS A) 20,160 B) 5040 C) 2520 D) 1260 12) LOOK A) 4 B) 16 C) 24 D) 12 13) BASEBALL A) 5040 B) 20,160 C) 10,080 D) 40,320 Given a group of students: or count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office. 14) Four representatives A) 1 B) 120 C) 10 D) 4 15) A male president and three representatives A) 3 B) 72 C) 6 D) 9 16) A treasurer and a secretary if the two must not be the same sex A) 3 B) 10 C) 12 D) 6 17) A president, a secretary, and a treasurer, if the president must be a woman and the other two must be men A) 12 B) 6 C) 3 D) 4 Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired. 18) Two accounting majors must be hired first, then one economics major, then two marketing majors. A) 4 ways B) 288 ways C) 24 ways D) 144 ways 19) There is no restriction on the college majors hired for the five positions. A) 3024 ways B) 24 ways C) 15,120 ways D) 120 ways 20) One accounting major, one economics major, and one marketing major would be hired, then the two remaining positions would be filled by any of the majors left. A) 48 ways B) 2160 ways C) 4320 ways D) 720 ways An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. 21) In how many ways can the people be presented? A) 2520 B) 5040 C) 49 D) 720 22) In how many ways can the men be presented first and then the women? A) 144 B) 2 C) 72 D) 5040 23) In how many ways can the first award be presented to Karen and the last to Lyle? A) 360 B) 840 C) 24 D) 120
Evaluate the combination. 24) A) 4 B) 56 C) 28 D) 10,080 25) A) 24 B) 2 C) 24! D) 24! - 10 26) 27) A) 1260 B) 5040 C) 1 D) 2520 A) 13! - 5 B) 13! C) 1 D) 2 Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the following cards? 28) All black cards A) 263,120 hands B) 131,560 hands C) 65,780 hands D) 32,890 hands 29) All hearts A) 3861 hands B) 143 hands C) 2574 hands D) 1287 hands 30) No face cards A) 658,008 hands B) 127,946 hands C) 639,730 hands D) 319,865 hands 31) Two black cards and three red cards A) 1,690,000 hands B) 845,000 hands C) 422,500 hands D) 1,267,500 hands Decide whether the situation involves permutations or combinations. 32) A batting order for 9 players for a baseball game. 33) An arrangement of 20 people for a picture. 34) A committee of 2 delegates chosen from a class of 26 students to bring a petition to the administration. 35) A sample of 10 items taken from 90 items on an assembly line. 36) A blend of 3 spices taken from 8 spices on a spice rack. 37) A selection of a chairman and a secretary from a committee of 15 people.
Solve the problem. 38) How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 52-card deck? A) 288 five-card hands B) 12 five-card hands. C) 6 five-card hands D) 24 five-card hands 39) A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 apples? A) 12 ways B) 6 ways C) 10 ways D) 24 ways 40) A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many ways can you get exactly 5 apples? A) 42 ways B) 210 ways C) 105 ways D) 1050 ways 41) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 oranges? A) 15 ways B) 5 ways C) 8 ways D) 0 ways 42) How many ways can a committee of 2 be selected from a club with 12 members? A) 66 ways B) 33 ways C) 2 ways D) 132 ways 43) In how many ways can a student select 8 out of 10 questions to work on an exam? A) 45 ways B) 90 ways C) 16 ways D) 100,000,000 ways 44) In how many ways can a group of 6 students be selected from 7 students? A) 1 way B) 7 ways C) 42 ways D) 6 ways 45) The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano? A) 931 ways B) 1001 ways C) 1071 ways D) 986 ways 46) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? A) 5665 ways B) 4620 ways C) 4410 ways D) 5170 ways A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 47) All cherry A) 0.1212 B) 0.3636 C) 0.7272 D) 0.1091 48) All orange A) 0.0182 B) 0.0061 C) 0.0011 D) 0.7272 49) All lemon A) 0.061 B) 1 C) 0 D) 0.1212 50) 2 cherry, 1 lemon A) 0.7272 B) 0.1212 C) 0.3636 D) 0.1818 51) One of each flavor A) 0.3636 B) 0.0667 C) 0.1818 D) 0.2182
52) 2 orange, 1 lemon A) 0.1091 B) 0.0364 C) 0.3636 D) 0.0303 53) 1 cherry, 2 lemon A) 0.0364 B) 0.3636 C) 0.0424 D) 0.0303 Solve. 54) A 6-sided die is rolled. What is the probability of rolling a number less than 3? A) B) C) D) 55) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10? A) 3 B) C) D) 56) A lottery game contains 29 balls numbered 1 through 29. What is the probability of choosing a ball numbered 30? A) B) 29 C) 0 D) 1
Give the probability distribution and sketch the histogram. 57) A class of 44 students took a 10-point quiz. The frequency of scores is given in the table. A) B) C) D)
58) Five rats are inoculated against a disease. After an incubation period, the number contracting the disease is noted. The experiment is repeated 20 times, with the results shown in the table. A) B) C) D)
Find the expected value for the random variable. 59) 60) A) 7.44 B) 9 C) 7.84 D) 7.76 A) 3.5 B) 4.5 C) 3.3 D) 3.9 61) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. A) 2.85 B) 2.98 C) 2.73 D) 3.01 62) For a certain animal species, the probability that a female will have a certain number of offspring in a given year is given in the table below. Find the expected number of offspring per year. A) 1.75 B) 1.58 C) 1.38 D) 2 Find the expected value for the random variable x having this probability function. 63) 64) A) 15.5 B) 12.7 C) 12.4 D) 16 A) 16 B) 13.4 C) 14.7 D) 13
65) A) 25.5 B) 25 C) 22.5 D) 27.5 Provide an appropriate response. 66) List the two requirements for a probability distribution. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram. 1) A 2) B 3) A 4) A 5) B 6) B 7) D 8) C 9) D 10) B 11) D 12) D 13) A 14) B 15) B 16) C 17) A 18) D 19) C 20) D 67) Discuss the differences, both in applications and in the formulas, for combinations and permutations. Give an example of each. 68) Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither? A) Combination B) Permutation C) Neither 69) Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither? A) Combination B) Permutation C) Neither 70) Consider the selection of officers for a club. Is this a combination, a permutation, or neither? A) Combination B) Permutation C) Neither