Name Date Class Practice A. 1. In how many ways can you arrange the letters in the word NOW? List the permutations.

Transcription

1 708 Name Date _ Class _ Practice A Permutations. In how many ways can you arrange the letters in the word NOW? List the permutations. 2. In how many ways can you arrange the numbers 4, 5, 6, and 7 to make a four-digit number? List the permutations. 3. Find the number of permutations of the letters in the word FOUR. 4. In how many ways can you arrange the numbers 3, 4, 5, 6, and 7 to make a five-digit number? 5. Find the number of ways you can arrange the letters in the word numbers. Choose the letter for the best answer. 6. What is another way of showing 5 factorial or 5!? A 5 3 B C D In how many ways can 5 children be matched with 5 puppies? A 5 C 00 B 25 D How many permutations of the numbers through 9 are there? A 9 C 9! B 900,000 D How many permutations of the numbers 0 through 4 are there? F 0! G 5! H 4! J 4! 9. Six friends are waiting in line at the movie theater. In how many different orders can they be standing in line? F 720 H 36 G 20 J 6. In how many different ways can seven drivers be matched up with seven rental cars? F 5,040 H 49 G 2,40 J 7

2 708 Name Date _ Class _ Practice B Permutations. Joe has homework assignments for math, Spanish, and history. In how many different orders can he do his homework? 2. Find the number of permutations of the letters in the word SMART. 3. In how many ways can you arrange the numbers 6, 7, 8, and 9 to make a four-digit number? 4. A table has 8 seats. In how many different ways can 8 people sit at the table? 5. Nine mountain bikers are on a bicycle trip. In how many possible ways can they follow each other? 6. Seven students are waiting in line at the cafeteria. In how many different orders can they be standing in line? 7. How many permutations of the letters A through F are there? 8. Ed, Martine, Sal, Carl, Paula, Terry, Ken, Leo, Ursula, and Jamie are in a race. In how many different orders can they finish? 9. Find the number of permutations of the letters in the word recognizably. 0. In how many different orders can people stand in line?. In how many different ways can a librarian arrange eight books on a shelf? 2. Melinda has 5 art trophies. Write an expression that shows how many different ways she can line up her trophies on a shelf.

3 708 Name Date _ Class _ Practice C Permutations. a. Find the number of permutations of the letters in the word BRAIN. b. If you choose one of the permutations at random, what is the probability that it will start with a vowel? 2. a. In how many ways can you arrange the numbers 4, 5, 6, 7, 8, and 9 to make a six-digit number? b. If you choose one of the six-digit numbers at random, what is the probability that the number will be less than 600,000? 3. Eight skydivers are on an airplane. In how many possible ways can they jump from the plane? 4. There are seven different flavors of yogurt at a supermarket. In how many different orders can they be lined up on the shelf? 5. How many permutations of the numbers through 9 are there? 6. In how many different ways can a video store arrange ten videos on a shelf? 7. Harrison has a collection of 25 antique teapots. Write an expression that shows in how many different ways he can display his teapots. Determine whether each problem involves permutations or combinations. 8. Elect four people to be president, vice president, secretary, and treasurer. 9. Order a three-topping pizza from a choice of eight toppings. 0. Decide how many ways you can put ten books on a shelf.. Organize 30 students into two-person doubles teams.

4 708 Name Date _ Class _ Review for Mastery Permutations A permutation is a selection of objects in a particular order. In how many ways can Allie, Bob, and Carl stand in a line? You can draw a tree diagram to find the number of permutations.. Complete the tree diagram. Allie Bob Carl Carl Allie Allie Bob Carl Bob Allie 2. Complete the list of the outcomes. Bob Carl Bob Carl Carl Allie Allie Carl Bob Allie Bob Allie You can also use multiplication to find the number of permutations. 3. Complete the multiplication. Choices for first in line Choices for second in line Choices for third in line Number of permutations 4. There are permutations for 3 people standing in line. You can find the probability that they will be standing in line alphabetically. 5. P(alphabetical order) number of alphabetical arrangements total number of permutations 6. Find the number of ways you can arrange the letters in the word MATH.

5 708 Name Date _ Class _ Challenge Factorial Fun Sometimes you can use the definition of factorial to simplify computations with factorials. Example: 8! 5!2! Simplify. Remember to use the order of operations.. (3 2)! 2. (4!)(2!) 3. (2 3)! ! ! 7! 6. 6! 4! 7. 5! 7! 8. 9! 7! 9. 8! 3!5! 0. 6! 2!4!. 9! 8!3! 2. 0! 8!4! 3. 8! 4!4! 4. 3!5! 4! 5.! 7!4! 6. 6!8! 7!5! 7. 2! 2! 3! 8. 3!3! 3 3! 9. 4! 3! ! 4! 2. 2!(3!) 22. 4! 3! 23. 4!(3!)(2!) ! 3

6 708 Name Date _ Class _ Problem Solving Permutations Write the correct answer.. Five snowboarders are competing in a half-pipe competition during the Winter Sports Festival. In how many different orders can the snowboarders compete? 2. In how many different orders can, Debbie, Brigitte, and Adam wait in line in the school cafeteria? What is the probability that they will be in alphabetical order? 3. In how many different orders can the science class study the planets Jupiter, Saturn, Uranus, and Neptune? What is the probability that they will study Saturn first? Choose the letter for the best answer. 5. Hannah, Javier, and Beth were the three qualifiers for a race. In how many different orders can they finish? What is the probability that Hannah or Beth will be first? A 3 orders; 3 B 3 orders; 2 3 C 6 orders; 3 D 6 orders; Six different prizes are being awarded to the winners of a contest. In how many different ways can the prizes be awarded? A 4,320 ways B 720 ways C 20 ways D 30 ways 4. The physical education teacher sets up 8 different exercise stations for the class to complete. In how many different orders can the stations be done? 6. Berto and 5 friends have ordered dinner at a restaurant. What is the probability that Berto will be served last? F G H J Jonathan will have math, English, history, social studies, and science each day next year. What is the probability that his classes will be in alphabetical order? F G 5 24 H J

7 708 Name Date _ Class _ Reading Strategies Make an Organized List An arrangement of objects in a certain order is called a permutation. How many different ways are there to arrange turkey, lettuce, and tomato on a sandwich? You can make a list of the items just as they would appear on the sandwich. If turkey is on top, the lettuce and tomato could be arranged as follows: Turkey Turkey Lettuce Tomato Tomato Lettuce Answer each question.. List the ways you can arrange the three items with lettuce on the top. 2. How many different arrangements are there with lettuce on top? 3. List the ways you can arrange the three items with the tomato on top. 4. Make an organized list showing all the different arrangements that can be made with turkey, lettuce, and tomato. 5. How many different ways can you arrange tomato, lettuce and turkey on a sandwich?

8 708 Name Date _ Class _ Puzzles, Twisters & Teasers Stay on Track! Across. A is an arrangement of objects or events in which the order is important. 5. In a permutation, each time you make a for one position, there is one less from which to choose. 7. The Counting Principle can help you find the number of permutations. 8. Permutations and are not the same. Down. The number of permutations of a group of objects may be written as a factorial. 2. The order of a group of objects may be chosen at. 3. An permutation is based on the letters in the names of the objects. 4. You can use a to find the number of permutations of a group of objects. 5. You can find the of 6 by multiplying

9 LESSON -8 Practice A. 6 ways; now, nwo, own, onw, won, wno ways; 4,567; 4,576; 4,657; 4,675; 4,756; 4,765; 5,467; 5,476; 5,647; 5,674; 5,746; 5,764; 6,457; 6,475; 6,547; 6,574; 6,745; 6,754; 7,456; 7,465; 7,546; 7,564; 7,645; 7, ways 5. 5, C 7. G 8. D 9. F 0. C. F Practice B. 6 orders ways 4. 40,320 ways ,880 ways 6. 5,040 orders ,628, ,00, ,96, ,320 ways 5. 5! Practice C 6. 4; 3; 2; ; 24 ways Challenge Problem Solving. 20 orders 2. 6 orders; 6. a. 20; b orders; ,320 orders 2. a. 720 ways; b ,320 ways 4. 5,040 orders , ,628,800 ways 7. 25! 8. permutations 9. combinations 0. permutations. combinations Review for Mastery. Bob; 2. Allie; Bob; Carl; Carl; Allie; Carl; Bob; Allie Bob; Carl 3. 3; 2; ; D 6. J 7. B 8. H Reading Strategies. lettuce, tomato, turkey; lettuce, turkey, tomato tomato, lettuce, turkey; tomato, turkey, lettuce 4. turkey, lettuce, tomato turkey, tomato, lettuce; lettuce, tomato, turkey lettuce, turkey, tomato; tomato, turkey, lettuce tomato, lettuce, turkey 5. 6 different ways

10 Puzzles, Twisters & Teasers