Redwood High School. Department of Mathematics Advanced Algebra Test S2 #6.

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1 Redwood High School. Department of Mathematics Advanced Algebra Test S2 #6. Hard Worker's name: Find the indicated probability. 1) Of the 69 people who answered "yes" to a question, 12 were male. Of the 99 people that answered "no" to the question, 7 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? 2) How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O? 1) 2) Find the value of the combination. 9) C(4,4) 9) 10) C(9,) 10) 11) How many 5-card poker hands consisting of 2's and two cards that are not 2's are possible in a 52-card deck? 12) A student must choose 1 of 4 mathematics electives, 1 of 5 science electives, and 1 of 9 programming electives. How many possible course selections are there? 11) 12) ) The town hall has 7 bells in its bell tower. Before sunset bells are rung in sequence. No bell is rung more than once. How many sequences are there? ) 1) From 8 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible? 1) Find the value of the permutation. 4) P(9, 1) 4) 5) P(, 0) 5) 14) 8 C 4 14) 15) 10! 15) 6) P(9, 9) 6) 7) 7 7 7) 8) A combination lock has 20 numbers on it. How many different -digit lock combinations are possible if no digit can be repeated? 8) 16) 5! 4!1! 17) In how many ways can a class president and a class secretary be chosen from a group of 10 candidates? 18) How many different vertical arrangements are there of 7 flags if are white, are blue, and 1 is red? 16) 17) 18) 1

2 19) 5!! 2! 20) How many different vertical arrangements are there of 8 flags if 4 are white, are blue, and 1 is red? Solve the problem. 21) Lisa has 4 skirts, 6 blouses, and 2 jackets. How many -piece outfits can she put together assuming any piece goes with any other? 22) Give the probability that the roll of a die will show 4 or 6. 2) A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11? 24) A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of? 25) A restaurant offers a choice of 4 salads, 5 main courses, and desserts. How many possible -course meals are there? 26) A salesman packed shirts and 6 ties. With one shirt, he could wear all 6 ties. With another shirt, he could wear 5 ties. With the other shirt, he could wear only ties. How many different combinations did he have? 19) 20) 21) 22) 2) 24) 25) 26) 27) A student is told to work any 6 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.) 28) Among a group of 69 investors, 21 owned shares of Stock A, 27 owned shares of Stock B, 29 owned shares of Stock C, 9 owned shares of both Stock A and Stock B, 9 owned shares of Stock A and Stock C, 1 owned shares of Stock B and Stock C, and 7 owned shares of all three. How many investors did not have shares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B? 27) 28) 29) 10! 29) 2! 0) In a survey of 17 vacationers in a popular beach resort town, 58 indicated they would consider buying a home there, 6 would consider buying a beach villa, 4 would consider buying a lot, 26 would consider both a home and a villa, 27 would consider both a home and a lot, 20 would consider both a villa and a lot, and 14 would consider all three. How many vacationers would not consider any of the three? How many would consider only a home? 0) 2

3 1)! 0!! 1) Use the information given in the figure. 9) 2) ) 4! 2! 2! 6! 5!1! 2) ) ) In a survey of 4 hospital patients, 18 said they nursing care, 20 said they medical treatment, and 5 said they were satisfied with both. How many patients were satisfied with neither? How many were satisfied with only the medical treatment? 4) 40) How many are in B but not in A? ) 4!!1! 5) How many are in set A? 6) Suppose there are 5 roads connecting town A to town B and 7 roads connecting town B to town C. In how many ways can a person travel from A to C via B? 6) 41) ) How many 2-digit numbers can be formed using the digits 1, 2,, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once. 8) Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw, 5, or 1? 7) 8) 42) How many are in B or C? How many are in B and C?

4 4) 9! 0!9! solve the problem. (2 points each) 44) One digit from the number 1,959,889 is written on each of seven cards. What is the probability of drawing a card that shows 1, 9, or 5? 45) A spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of? 46) 8! 8!0! 4) 44) 45) 46) evaluate the expression without a calculator. (2 points ) 47) 1 C 4 47) 48) 49) 9! 1!8! 9! 7! 2! solve the problem. 50) Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 6, 8, or 4? 48) 49) 50) 51) In a student survey, 94 they speak Spanish, they speak French, 10 they speak both Spanish and French, and 19 they speak neither. How many students participated in the survey? 52) In a survey of 51 hospital patients, 2 said they nursing care, 20 said they medical treatment, and 6 said they were satisfied with both. How many patients were satisfied with neither? How many were satisfied with only the medical treatment? 51) 52) 5) 10 P 5 5) 54) 6 P 5 54) Evaluate the expression by hand (no calculator). 55) C(12, 6) 55) 56) 9! 56) 7! 57) 10 P 57) Evaluate the expression by hand (no calculator). 9 58) 5 58) 4

5 59) A state lottery involves the random selection of six different numbers between 1 and 27. If you select one six number combination, what is the probability that it will be the winning combination? 60) How many different 11-letter words (real or imaginary) can be formed from the letters in the word ENGINEERING? 61) Among a group of 66 investors, 21 owned shares of Stock A, 24 owned shares of Stock B, 2 owned shares of Stock C, 11 owned shares of both Stock A and Stock B, 9 owned shares of Stock A and Stock C, 15 owned shares of Stock B and Stock C, and 7 owned shares of all three. How many investors did not have shares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B? 62) Using the numerals 0 through 9, how many 6-digit serial numbers can be made if the first digit must be 0 or 1 and numerals may be repeated? 59) 60) 61) 62) 64) In a survey of 159 vacationers in a popular beach resort town, 40 indicated they would consider buying a home there, 70 would consider buying a beach villa, 48 would consider buying a lot, 20 would consider both a home and a villa, 19 would consider both a home and a lot, 17 would consider both a villa and a lot, and 9 would consider all three. How many vacationers would not consider any of the three? How many would consider only a home? 65) There are 10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? 66) How many different 8-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once? 64) 65) 66) 6) How many different 10-letter words (real or imaginary) can be formed from the letters in the word IMMUNOLOGY? 6) 5

6 Answer Key Testname: ADVALG S2 TEST 2 WKS PERMUTATIONS V5LONG. 1) ),800 ) 210 4) 9 5) 1 6) 62,880 7) 1 8) ) 1 10) 84 11) ) 180 course selections 1) 56 14) 70 15),628,800 16) 5 17) 90 18) ) 10 20) ) 48 possible outfits 22) 1 2) ) 2 25) 60 possible meals 26) 14 combinations 27) ) 16; 26 29) 1,814,400 0) 2; 19 1) 1 2) 6 ) 6 4) 10; 15 5) 4 6) 5 7) 90 8) 10 9) 28 40) 40 41) 48 42) 8 4) 1 44) 5 7 6

7 Answer Key Testname: ADVALG S2 TEST 2 WKS PERMUTATIONS V5LONG. 45) 2 46) 1 47) 1,465 48) 9 49) 6 50) 10 51) ) 14; 14 5) 0,240 54) ) ) 72 57) ) ) 296,010 60) 277,200 61) 17; 25 62) 200,000 6) 907,200 64) 48; 10 65) ) 62,880 7

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