MDM4U Exam Review - Ch. 5 Combinations

MDM4U Exam Review - Ch. 5 CombinationsMultiple ChoiceIdentify the letter of the choice that best completes the statement or answers the question.1. There are 8 students on the curling team and 12 students on the badminton team. What is the total number ofstudents on the two teams if three students are on both teams?a. 20c. 15b. 17d. 142. An amateur drama group has 15 volunteers for backstage work and 11 for the box office. If 6 volunteers arewilling to work either backstage or in the box office, how many volunteers are there altogether?a. 17c. 20b. 19d. 263. Of the 20 players on the Statsville hockey team, 5 play both defence and forward, 2 play only in goal, and 6play only forward. If no one on the team plays both goal and another position, how many players play onlydefence?a. 5c. 9b. 7d. 114. The value C(15, 4) isa. 1365c. 3003b. 36 036d. 32 7605. The value 21C18 isa. 1365c. 1330b. 378d. 27606. The number of combinations of eight items taken three at a time can be written asa. C(3, 8)c. P(8, 3)b. C(8, 3)d. C(8-3)7. How many different sums of money can you make with three coins of different denominations?a. 8c. 7b. 3d. 48. If a cartoonist has pens with five different colours of ink, how many different combinations of colours couldthe cartoon have?a. 32c. 25b. 5d. 319. In how many ways can you have a snack if you find three apples, two bananas, and four cookies on thekitchen counter?a. 24c. 60b. 9d. 5910. How many different sums of money can you make with a penny, a nickel, a dime, and a quarter?a. 7c. 12b. 11d. 15Short Answer11. A video store has a window display of new releases and the staff’s top-five picks. If there are eight newreleases this week and three of them are on the staff’s top-five list, how many different videos are in thewindow display? Illustrate your answer with a Venn diagram.

12. There are 10 students on the basketball team, 11 students on the soccer team, and 14 students on thevolleyball team. Only 3 students play on all three teams, but 5 students play both soccer and volleyball, 4 playboth volleyball and basketball, and 7 play both soccer and basketball. What is the total number of students onthe three teams? Illustrate your answer with a Venn diagram.13. Of the 19 employees at a gift shop, 13 work full time, 7 work on weekends, and 9 are casual employees. Allof the permanent part-time employees work on weekends, 3 of the full-time employees work on weekends, 4of the casual employees work full time, and 4 of the weekend staff are casual employees. Use a Venn diagramto determine how many full-time casual employees work on weekends.14. Of the 73 books in a sale bin, 33 are fiction, 41 are Canadian, and 35 are about the military. All of the salebooks fit at least one of the three categories. If 12 of these books are Canadian fiction, 17 are about theCanadian military, and 16 are military fiction, how many of the books fit in all three categories? Use a Venndiagram to illustrate your answer.15. A translation service has 33 employees, of whom 27 speak French, 11 speak Spanish, and 7 speak Hindi. Ofthe Spanish-speaking employees, 5 speak Hindi and 6 speak French, but only 3 of the French-speakingemployees speak Hindi. All of the employees speak at least one of these three languages. Use a Venn diagramto determine how many of the employees speak all three.16. A day-care worker is choosing four games for the children to play. How may sets of games could the workerchoose if the centre has nine games available?17. The game of euchre uses just the 9s, 10s, jacks, queens, kings, and aces from a standard deck of 52 cards.How many five-card euchre hands have all black cards?18. All 16 people at a function shake hands with everyone else at the function. Use combinations to find the totalnumber of handshakes.19. The Statsville hockey team has nine forwards, nine defenders, and two goalies. Use combinations todetermine the number of ways the team can form a line-up of three forwards, two defenders, and one goalie.20. A quilter has 15 different squares made up, 8 with blue as the main colour, 4 with gold, and 3 with green.What is the total number of ways the quilter can choose 2 squares of each colour for a table runner?21. The group organizing the Statsville College reunion includes 6 current students, 8 current staff members, and11 alumni. Two individuals from each category will work on the publicity committee. Use combinations todetermine the number of different publicity committees the group could form.22. How many different sums of money can you make with three pennies, a nickel, a dime, and two quarters?23. How many different sums of money can you make with four pennies, two nickels, and six quarters?24. In how many ways can a six-member committee form a subcommittee with at least two members?25. Susan’s company has just won an important new contract. She will have to assign a project team of at least 4of her 11 staff members to this contract in order to complete it on time. If no more than 5 staff members canbe spared from other work, how many different project teams could Susan form for the new contract?Problem

26. Of the 190 students graduating from Statsville High School, 111 played on a sports team, 26 served on thestudents’ council, and 67 were members of clubs. Only 10 students did not participate in any of theseactivities. If 13 students were members of both a team and a club, 9 were on both a team and the students’council, and 11 were members of both the students’ council and a club, how many graduating students havebeen a member of a team as well as the students’ council and a club? Illustrate your answer with a Venndiagram.27. Josh is conducting a telephone survey for a telecommunications company. Over the course of a 4-h shift, helogged the following calls:16 to single-family homes21 to homes with more than one telephone line17 to people who were satisfied with their current long-distance provider11 to people who lived in single-family homes and were satisfied with their current long-distance provider7 to single-family homes with more than one telephone line9 to people who were satisfied with their long-distance provider and had more than one line4 to people who lived in single-family homes, had more than one line, and were satisfied with theirlong-distance provider5 to people who lived in multi-family buildings, had only one line, and were unhappy with their currentlong-distance providerHow many calls did Josh make in this shift? Illustrate your answer with a Venn diagram.28. Of 24 condominium buildings in a retirement community, 12 have a swimming pool, 11 have tennis courts,and 15 have a room for playing cards. All the buildings have at least one of these amenities. If 4 buildingshave a pool and tennis courts, 5 have a pool and a card room, and 3 have all three, how many of the buildingshave tennis courts and a card room but no pool? Illustrate your answer with a Venn diagram.29. A fabric store has 44 bolts of fabric on its clearance table. Of these bolts, 28 are broadcloth, 17 are floralprints, 20 have a blue background, 12 are floral prints on broadcloth, 10 are broadcloth with a bluebackground, and 4 are floral prints with a blue background. If all but 2 of the clearance fabrics fit at least oneof these categories, how many of the bolts are broadcloth floral prints with a blue background? Illustrate youranswer with a Venn diagram.30. Statsville’s baseball club has one pitcher, two catchers, three short-stops, five infielders, and five outfielders.How many different ways could the team fill the starting roster of one pitcher, one catcher, one short-stop,three infielders, and three outfielders? Explain your reasoning.31. A 15-passenger shuttle bus takes athletes between venues at the Canada Summer Games. If 32 athletes needto get to the track and field stadium, in how many ways can passengers be chosen fora) the bus’s first trip?b) the bus’s second trip?32. For the upcoming musical, the director has auditioned eight singers suitable for the three male principal rolesand ten singers suitable for the four female principal roles. In how many different ways can the director castthe principal roles for this show?33. A project team of up to 5 people is being formed from a staff of 15. How many such teams are possible?34. An athletic committee with three members is to be selected from a group of six gymnasts, five weightlifters,and seven sprinters. In how many ways can the committee be selected if it must include at least oneweightlifter? Explain your reasoning.

35. The director of a play has found five flute solos, two guitar pieces, and three violin pieces that would work asbackground music for some of the scenes. There has to be some violin music because it is mentioned in theplay. In how many ways can the director choose the three pieces of music for the play? Explain yourreasoning.

MDM4U Exam Review - Ch. 5Answer SectionMULTIPLE CHOICE1. ANS:LOC:2. ANS:LOC:3. ANS:LOC:4. ANS:LOC:5. ANS:LOC:6. ANS:LOC:7. ANS:LOC:8. ANS:LOC:9. ANS:LOC:10. ANS:LOC:BREF:CP1.01, CP1.02CREF:CP1.01, CP1.02BREF:CP1.01, :CREF:CP1.02, CP1.06DREF:CP1.02, CP1.06DREF:CP1.02, CP1.06DREF:CP1.02, CP1.06Knowledge & UnderstandingOBJ: Section 5.1TOP: Organized countingKnowledge & UnderstandingOBJ: Section 5.1TOP: Organized countingKnowledge & UnderstandingOBJ: Section 5.1TOP: Organized countingKnowledge & UnderstandingOBJ: Section 5.2Evaluating combinationsKnowledge & UnderstandingOBJ: Section 5.2Evaluating combinationsKnowledge & UnderstandingOBJ: Section 5.2Evaluating combinationsKnowledge & UnderstandingOBJ: Section 5.3TOP: Applying combinationsKnowledge & UnderstandingOBJ: Section 5.3TOP: Applying combinationsKnowledge & UnderstandingOBJ: Section 5.3TOP: Applying combinationsKnowledge & UnderstandingOBJ: Section 5.3TOP: Applying combinationsSHORT ANSWER11. ANS:10 videosREF: Applications OBJ: Section 5.1LOC: CP1.01, CP1.02TOP: Venn diagrams12. ANS:There is a total of 22 students on the three teams.

REF: Applications OBJ: Section 5.1LOC: CP1.01, CP1.02TOP: Venn diagrams13. ANS:There is only 1 casual full-time employee who works on weekends.REF: Applications OBJ: Section 5.1LOC: CP1.01, CP1.02TOP: Venn diagrams14. ANS:There are 9 books that fit in all three categories.

REF: Applications OBJ: Section 5.1LOC: CP1.01, CP1.02TOP: Venn diagrams15. ANS:There are 2 employees who speak all three of the languages.REF: Applications OBJ: Section 5.1TOP: Venn diagrams16. ANS:9C4 126LOC: CP1.01, CP1.02REF: Applications OBJ: Section 5.2TOP: Applying combinations17. ANS:12C5 792LOC: CP1.04, CP1.06REF: Applications OBJ: Section 5.2TOP: Applying combinations18. ANS:16C2 120LOC: CP1.04, CP1.06REF: Applications OBJ: Section 5.2TOP: Applying combinations19. ANS:9C3 ! 9C2 ! 2C2 6048There are 6048 possible line-ups.LOC: CP1.04, CP1.06REF: Applications OBJ: Section 5.2TOP: Applying combinations20. ANS:8C2 ! 4C2 ! 3C2 504LOC: CP1.02, CP1.04, CP1.06REF: Applications OBJ: Section 5.2TOP: Applying combinations21. ANS:6C2 ! 8C2 ! 11C2 23 100LOC: CP1.02, CP1.04, CP1.06