Counting practice permutation and combinations PDF

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Practice notes for permutation and combinations...

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Math 120, Chapter 6, Counting Worksheet on permutation, combinations, and neither 1) A particular model of car is available in 3 body styles, 8 exterior colors, and 10 interior colors. How many different cars of this model can be ordered? 2) A pizza restaurant has 4 different meat toppings and 6 different vegetable toppings from which to choose. a) How many ways are there to order a single topping pizza? b) How many ways are there to order a pizza with one meat topping and one vegetable topping?

3) You are selecting a new cell phone and a cell phone plan from your wireless carrier. You must choose from 1 of 5 different cell phone plans and you have two different models of phones from which to choose. One model comes in 4 different colors and the other model comes in 3 different colors. How many ways can you select a new phone and a new plan?

4) A questionnaire consists of 4 questions to be answered “always”, “often”, “sometimes”, “seldom”, or “never”. a) How many ways can the questionnaire be completed if each question must be answered? b) How many ways can the questionnaire be completed if one or more questions may be left blank? 5) a) How many permutations are there of the letters A, B, C, and D taken two at a time? List them all. b) How many combinations are there of the letters A, B, C, and D taken two at a time? List them all. 6) Twenty applicants are to be interviewed for a position, and then the field will be narrowed down to the top five candidates. a) How many possible results are there if the interviewer ranks his or her top five candidates in order of preference? b) How many possible results are there if the interviewer selects a pool of his or her top five candidates leaving them unranked? 7) A newly formed consumer action group has thirty members. a) How many ways can the group elect 4 different members to be president, vice president, secretary, and treasurer? b) How many ways can the group elect 4 different members to form an executive committee?

Math 120, Chapter 6, Counting Worksheet on permutation, combinations, and neither 8) Five people are eligible to receive awards. a) How many ways can the awards be given if there are two identical awards and they must go to two different people? b) How many ways can the awards be given if there are two different awards and they must go to two different people? c) How many ways can the awards be given if there are two different awards and the same person may receive both awards? 9) At a certain pizza parlor a pizza can be ordered with any of the following toppings: Canadian bacon, sausage, pepperoni, green pepper, onion, and mushroom. a) How many different pizzas can be ordered with two different toppings? b) How many different pizzas can be ordered with three different toppings? c) How many different pizzas can be ordered with four different toppings?

10) There are 16 different volumes of an encyclopedia. They are numbered 1 through 16. a) How many different ways are there to line up all of the volumes on a shelf? b) How many different ways are there to select six of the volumes and then line them up on a shelf? 11) There are 12 horses entered into a horse race. a) How many ways are there for you to place a bet where you must pick the first 3 horses finishing the race but you do not have to pick the precise order of their finish? b) How many ways are there for you to place a bet where you must pick the first 3 horses finishing the race and pick the precise order of their finish? 12) There are 4 women and 8 men eligible to serve on a 6-person committee. a) How many committees are possible? b) How many committees are possible that contain no women? c) How many committees are possible that contain exactly one woman? d) How many committees are possible that contain at most one woman? e) How many committees are possible that contain at least one woman? 13) A university committee consists of 4 students, 7 faculty members, 3 administrators, and 2 civil service employees. A subcommittee of 5 members is to be selected. a) How many subcommittees are possible that contain only faculty members? b) How many subcommittees are possible that contain no faculty members? c) How many subcommittees are possible that contain exactly 2 faculty members and 1 administrator? d) How many subcommittees are possible that contain at least one civil service employee and no administrators?

Math 120, Chapter 6, Counting Worksheet on permutation, combinations, and neither 14) There are 4 women and 8 men eligible for awards. No person can get two awards. a) How many ways can four identical awards of $100 each be given? b) How many ways can four awards of $300, $200, $100, and $50 be given? c) How many ways can three awards of $300, $200, and $100 be given if the $300 and $100 awards must go to women? 15) An ice cream parlor has 3 flavors of hard ice cream: chocolate, vanilla, and strawberry. How many ways can you order a cone with two scoops if a) you must select 2 different flavors and chocolate on top of vanilla is considered different from vanilla on top of chocolate? List all of the possibilities. b) you must select 2 different flavors and chocolate on top of vanilla is not considered different from vanilla on top of chocolate? List all of the possibilities. c) you may select the same flavor for both scoops and chocolate on top of vanilla is considered different from vanilla on top of chocolate? List all of the possibilities. d) you may select the same flavor for both scoops and chocolate on top of vanilla is not considered different from vanilla on top of chocolate? List all of the possibilities. 16) An ice cream parlor has 10 flavors of hard ice cream. How many ways can you order a cone with two scoops if a) you must select 2 different flavors and chocolate on top of vanilla is considered different from vanilla on top of chocolate? b) you must select 2 different flavors and chocolate on top of vanilla is not considered different from vanilla on top of chocolate? c) you may select the same flavor for both scoops and chocolate on top of vanilla is considered different from vanilla on top of chocolate? d) you may select the same flavor for both scoops and chocolate on top of vanilla is not considered different from vanilla on top of chocolate?

Math 120, Chapter 6, Counting Worksheet on permutation, combinations, and neither Answers: 1) 3 8 10 240 2) a) 4  6 10 b) 4 6 24 3)  3  4  5 35 4) a) 5 5 5 5 625 b) 6 6 6 6 1296 5) a) P(4, 2) = 12: AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC 5) b) C(4, 2) = 6: AB, AC, AD, BC, BD, CD 6) a) P(20, 5) = 1,860,480 b) C(20, 5) = 15,504 7) a) P(30, 4) = 657,720 b) C(30, 4) = 27,405 8) a) C(5, 2) = 10 b) P(5, 2) = 20 c) 5 5 25 9) a) C(6, 2) = 15 b) C(6, 3) = 20 c) C(6, 4) = 15 10) a) P(16, 16) = 16! ≈ 2.0923 *1013 b) P(16, 6) = 5,765,760 11) a) C(12, 3) = 220b) P(12, 3) = 1320 12) a) C(12, 6) = 924 b) C(8, 6) = 28 c) C 4, 1 C 8, 5 224 12) d) C 8, 6  C 4, 1 C 8, 5 252 e) C 12, 6  C 8, 6 896 13) a) C(7, 5) = 21 b) C(9, 5) = 126 c) C 7, 2 C 3, 1 C 6, 2 945 13) d) C 2, 1 C 11, 4  C 2, 2 C 11, 3 825 14) a) C(12, 4) = 495 b) P(12, 4) = 11,880 c) 4 3 10 120 15) a) CV, VC, CS, SC, VS, SV P(3, 2) = 6 15) b) CV, CS, VS C(3, 2) = 3 3 3 9 15) c) CC, CV, CS, VV, VC, VS, SS, SC, SV 3  C 3, 2  6 15) d) CC, VV, SS, CV, CS, VS 16) a) P(10, 2) = 90 b) C(10, 2) = 45 c) 10 10 100 d) 10  C 10, 2  55...