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How much should I invest?

How much should I invest?.

kenishaj
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How much should I invest?

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  1. How much should I invest? • I got the perfect investment offer. For the last 10 weeks I received a share recommendation from a fund manager, telling me whether a stock’s price would rise or fall over the next week. After ten weeks, all the recommendations were proved right. So, he predicted the future 10 times in a row. There is only a one-in-a-thousand chance that the result is down to luck. I think this guy is a genius. I plan to invest all my kids’ college money. What do you think?

  2. The Math

  3. This is a well-known scam. The promoter sends out 100,000 e-mails, picking a stock at random. Half the recipients are told that the stock will rise; half that it will fall. After the first week, the 50,000 who received the successful recommendation will get a second e-mail; those that received the wrong information will be dropped from the list. And so on for ten weeks. At the end of the period, just by the law of averages, there should be 98 punters convinced of the manager’s genius and ready to entrust their savings

  4. The Math

  5. WARMUP 1. 5 4 3 2 1 7 6 5 4 3 2 1 6 5 4 3 2 1 2 3 2. Lesson 10.1, For use with pages 682-689 Evaluate the expression. Hint: NO Calculator 120 ANSWER 7/6 ANSWER 3. The number of choices Meghan has for displaying her trophies is represented by the expression a • b. If a = 4 and b = 3, how many choices does Meghan have? 12 ANSWER 4. How many different 4-digit bank pin numbers are there? 10,000 ANSWER

  6. 10.1 Notes - Counting Principal & Permutations Fictitious Vampires Duke it Out

  7. Objective -To count the number of ways an event can happen.

  8. How many possible 7-digit phone numbers are there if the first digit cannot be 0 or 1?

  9. A multiple choice test has 6 questions with 5 choices each. In how many ways can you complete the test?

  10. How many three-digit numbers greater than 500 can be formed from the digits 1, 2, 5, 7 and 9 if no repetition is allowed? 4 3 3 5,7,9 How many positive three-digit even numbers can be formed without using the digits 0, 1, 2, 3 or 4? 2 5 5 5-9 5-9 6,8

  11. A certain state has license plates that are made of four numbers followed by two letters? How many different license plates are possible if no repeated letters or numbers are allowed?

  12. !

  13. Say “Factorial”When you see “!”, say Factorial. It means to multiply that number by all the positive integers less than it. Your calculator has a “button” for it. I suggest you find it. Graphing calculators, look under “Math”

  14. Permutation- is an ordering of n objects. How many permutations are there for the letters in the word CAT? CAT, CTA, ACT, ATC, TCA, TAC = 6 How many permutations are there for the letters in the word CAT?

  15. There are 9 songs on your MP3 player. In how many different ways could you listen to these songs? If you only had time to listen to 3 of the 9 songs on your MP3 player, how many different ways could you listen to these 3 songs?

  16. In how many different ways can the letters in the word TRIANGLE be arranged? How many different ways could 10 runners finish in first, second and third place?

  17. Find the number of permutations of 7 objects taken 4 at a time.

  18. Find the number of permutations for the letters in the word STREET.

  19. Find the number of permutations for the letters in the word MATHEMATICS. Find the number of permutations for the letters in the word SLEEPLESS.

  20. By Definition…Write it down!!!! 0! = 1

  21. Snowboarding A sporting goods store offers 3 types of snowboards (all-mountain, freestyle, and carving) and 2 types of boots (soft and hybrid). How many choices does the store offer for snowboarding equipment? EXAMPLE 1 Use a tree diagram Do this one!!!! SOLUTION Draw a tree diagram and count the number of branches.

  22. ANSWER The tree has 6 branches. So, there are 6 possible choices. EXAMPLE 1 Use a tree diagram

  23. Photography You are framing a picture. The frames are available in 12 different styles. Each style is available in 55 different colors. You also want blue mat board, which is available in 11 different shades of blue. How many different ways can you frame the picture? EXAMPLE 2 Use the fundamental counting principle

  24. ANSWER The number of different ways you can frame the picture is 7260. = 7260 = 125511 Number of ways EXAMPLE 2 Use the fundamental counting principle SOLUTION You can use the fundamental counting principle to find the total number of ways to frame the picture. Multiply the number of frame styles (12), the number of frame colors (55), and the number of mat boards (11).

  25. How many different license plates are possible if letters and digits can be repeated? How many different license plates are possible if letters and digits cannot be repeated? EXAMPLE 3 Use the counting principle with repetition License Plates The standard configuration for a Texas license plate is 1 letter followed by 2 digits followed by 3 letters.

  26. There are 26choices for each letter and 10choices for each digit. You can use the fundamental counting principle to find the number of different plates. = 261010262626 Number of plates ANSWER With repetition, the number of different license plates is 45,697,600. EXAMPLE 3 Use the counting principle with repetition SOLUTION = 45,697,600

  27. If you cannot repeat letters there are still 26choices for the first letter, but then only 25remaining choices for the second letter, 24choices for the third letter, and 23choices for the fourth letter. Similarly, there are 10choices for the first digit and 9choices for the second digit. You can use the fundamental counting principle to find the number of different plates. = 26109252423 Number of plates Without repetition, the number of different license plates is 32,292,000. ANSWER EXAMPLE 3 Use the counting principle with repetition = 32,292,000

  28. SPORTING GOODS The store in Example 1 also offers 3 different types of bicycles (mountain, racing, and BMX) and 3 different wheel sizes (20in.,22 in., and 24in.). How many bicycle choices does the store offer? ANSWER 9 bicycles for Examples 1, 2 and 3 GUIDED PRACTICE

  29. WHAT IF?In Example 3, how do the answers change for the standard configuration of a New York license plate, which is 3 letters followed by 4 numbers? ANSWER • The number of plates would increase to 175,760,000. • The number of plates would increase to 78,624,000. for Examples 1, 2 and 3 GUIDED PRACTICE

  30. In how many different ways can the bobsledding teams finish the competition? (Assume there are no ties.) In how many different ways can 3 of the bobsledding teams finish first, second, and third to win the gold, silver, and bronze medals? EXAMPLE 4 Find the number of permutations Olympics Ten teams are competing in the final round of the Olympic four-person bobsledding competition.

  31. There are 10! different ways that the teams can finish the competition. = 10 987654 3 2 1 10! Any of the 10teams can finish first, then any of the remaining 9teams can finish second, and finally any of the remaining 8teams can finish third. So, the number of ways that the teams can win the medals is: = 720 1098 EXAMPLE 4 Find the number of permutations SOLUTION = 3,628,800

  32. ANSWER The number of ways to finish would increase to 479,001,600. The number of ways to finish would increase to 1320. for Example 4 GUIDED PRACTICE WHAT IF?In Example 4, how would the answers change if there were 12 bobsledding teams competing in the final round of the competition?

  33. = 11,880 12! 12! 479,001,600 12P4 = = = 8! 40,320 ANSWER ( 12 – 4 )! You can burn 4 of the 12 songs in 11,880 different orders. EXAMPLE 5 Find permutations of n objects taken r at a time Music You are burning a demo CD for your band. Your band has 12 songs stored on your computer. However, you want to put only 4 songs on the demo CD. In how many orders can you burn 4 of the 12 songs onto the CD? SOLUTION Find the number of permutations of 12objects taken 4at a time.

  34. 5P3 4P1 ANSWER = 60 8P5 = 6720 ANSWER ANSWER = 4 for Example 5 GUIDED PRACTICE Find the number of permutations.

  35. 12P7 ANSWER = 3,991,680 for Example 5 GUIDED PRACTICE Find the number of permutations.

  36. Find the number of distinguishable permutations of the letters in MIAMI and TALLAHASSEE. MIAMI has 5letters of which M and I are each repeated 2times. So, the number of distinguishable permutations is: 5! 120 = = 30 2 2 2! 2! EXAMPLE 6 Find permutations with repetition SOLUTION

  37. TALLAHASSEE has 11letters of which A is repeated 3times, and L, S, and E are each repeated 2times. So, the number of distinguishable permutations is: 39,916,800 11! = 6 2 2 2 3! 2! 2! 2! EXAMPLE 6 Find permutations with repetition = 831,600

  38. MALL ANSWER 12 for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

  39. KAYAK ANSWER 30 for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

  40. ANSWER 50,400 CINCINNATI for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

  41. 10.1 Assignment 10.1: 3 OR 5 (Tree Diagrams – look at example 1 in the book and check your answer in the back), 13-53 EOO, 65 (WP in the back), 73,75 Team Count!!

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