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BASIC ALGEBRA 2 REVIEW 11.1 – 11.3 1. Evaluate 7! NAME ___________________ 2. 5040 3. Evaluate 2 P2 Evaluate 3! 6 4. 2 Evaluate 9 P5 . 15,120 5. If you toss 3 pennies, how many different outcomes are possible? 6. In a sailboat race, four boats are headed for the finish line. How many different ways can the four boats finish the race? 8=2∙2∙2 24 = 4! 7. Three six-sided dice are tossed. How many different number combinations can be formed if no numbers are repeated? 120 = 6 ∙ 5 ∙ 4 = 6P3 8. There are 10 players on the basketball team and 5 different positions to play. How many ways can Coach Mastenbrook fill the positions? 9. Helga has 3 soccer trophies, 4 basketball trophies, 2 tennis trophies, and 1 golf trophy. How many different ways can she arrange the trophies in a row on her shelf? (The trophies don’t have to be grouped by category.) 30,240 = 10 P 5 10 total trophies so 10! or 3,628,800 10. Helga has 3 soccer trophies, 4 basketball trophies, 2 tennis trophies, and 1 golf trophy. How many different ways can she arrange the trophies in a row on her shelf if she puts the soccer trophies first, then the basketball trophies, then the tennis trophies, and finally the golf trophy? 24 = 3 ∙ 4 ∙ 2 ∙ 1 11. How many ways can 8 different glass beads be strung on a bracelet? 40,320 = 8! 12. Greg is planning a large dinner banquet. Guests can choose chicken, fish, or steak for their main course. Potatoes or rice for a side dish; and mixed vegetables, green salad, or coleslaw as a vegetable. How many dinner combinations can be made? 18 = 3 ∙ 2 ∙ 3 13. If 6 six-sided dice are tossed, how many different number combinations can there be if no numbers are repeated? 720 = 6! = 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 6 P 6 14. Write 4! in n(n 1)! form. 4 ∙ 3! 15. Write 35! in n(n 1)! form. 35 ∙ 34! 16. A baseball coach is deciding how to arrange the batting order of his 9 starting players. How many different batting orders are possible? 362,880 = 9! = 9 P 9 17. How many different ways can the letters in the word factor be arranged? 720 = 6! = 6 P 6 18. An ice cream shop sells ice cream in 3 different sizes. They have 16 flavors, 15 toppings, and 8 flavored syrups to choose from. How many different kinds of ice cream sundaes can you make if they each have one topping and one kind of syrup? 5760 = 3 ∙ 16 ∙ 15 ∙ 8 19. Raul is flying from San Francisco to Missoula, Montana. Three different airlines fly the route. Each airline offers 8 flights a day. Raul can choose between first class, business class, or coach class. How many different travel arrangements can Raul make? 72 = 3 ∙ 8 ∙ 3 20. Long ago, ships sent coded messages to other ships by displaying a sequence of different shaped flags. If a ship has a collection of 10 differently shaped flags, how many different messages of a four-flag sequence could be made? 5040 = 10 P 4