Combinatorics Review Assignment PDF

COMBINATORICS - REVIEW ASSIGNMENT Name: Date: My Achievement Goal for this chapter is… (Circle one) A+ A B C D This Assignment is: Good to Go...

COMBINATORICS - REVIEW ASSIGNMENT Name: Date: My Achievement Goal for this chapter is… (Circle one) A+ A B C D This Assignment is: Good to Go Needs Corrections Remember – show your work! Some of the answers are on the last page – what we want to see is all your work. Otherwise you may find things written in the “Needs Corrections” Box. J 1. A restaurant offers 4 different soft drink flavors, 5 different sandwiches and 3 different dessert selections. In how many ways can a person select one item from each category (a drink, a sandwich and a dessert)? 2. Licence plates for vehicles in a European country consist of the letter I or O, followed by any three digits, the first of which cannot be a zero, followed by any two letters which are not repeated. How many different vehicle license plates can be produced? 3. There are two routes from Picture River to Quattroville, three routes from Quattroville to St.Thomas, four routes from Picture River to Rushmore, and one route from Rushmore to St. Thomas. a) How many routes are there from Picture River to St. Thomas passing through Quattroville? b) How many routes are there from Picture River to St. Thomas? Page 1  COMBINATORICS - REVIEW ASSIGNMENT 4. How many ways can a sports team select a Manager, Fundraising Coordinator, Secretary, and Treasurer from a group of 28 parents, if they are all equally qualified for any position? 5. How many permutations are there of all the letters in KALAMALKA? 6. In how many ways can 5 senior citizens form a group of 8 be seated in a row of 5 chairs? (Use n Pr notation in your solution) 7. A nearby city council has created a sub-committee of seven council members to look at how the environment has been impacted by recent industrial development on city land. There are a total of 15 city council members, 9 males and 6 females. The sub-committee must consist of exactly 3 females. (Use n Cr notation in your solutions) a) Determine the number of ways of selecting i) the females ii) the males iii) the sub-committee b) In how many ways can the sub-committee be selected if Rachelle, the city mayor, must be included? 8. A drive-in movie theatre is open from dusk until dawn, showing five movies one Friday night. There are fourteen different movies available to show of which ten are disaster movies and four are horror movies. How many possible schedules of movies include: a) at least one horror movie? b) at least four disaster movies? Page 2  COMBINATORICS - REVIEW ASSIGNMENT 9. Caitlin wants to visit Shannon. Streets are shown as lines on the grid. Only north and east travel directions can be used. How many different paths can Caitlin take to get to Shannon? 10. What is the second number in the 80th row of Pascal's triangle? 11. How many terms are there in the expansion of ( x + y)12? (HINT: DO NOT EXPAND!) 12. Expand (a - 2)5 using the binomial theorem. 13. What is the seventh term in the expansion of (b + 5)13? Page 3 COMBINATORICS - REVIEW ASSIGNMENT Answers for some of the questions are shown below. --- YOU DO NOT HAVE TO UPLOAD THIS PAGE --- 1. 60 2. 1 170 000 3. a) 6 b) 10 4. 491 400 5. 3 780 6. 6 720 7. a) i) 20 ii) 126 iii) 2 520 b) 1260 8. a) 1750 b) 1092 9. 180 10. 1,360 11. 13 12. 𝑎! − 10𝑎" + 40𝑎# − 80𝑎$ + 80𝑎 − 32 13. 26 812 500 𝑏% Page 4