1. Do Now 1. Find the number of permutations with 7 books taken 4 at a time. 2. Find the number of permutations of the letters in each word: TennesseeGeorgiaAlabama

2. Pg. 640-641; 9-50 all 9. 4,920 10. 696 11. 2 12. 2 13. 56 14. 210 15. 20 16. 720 17. 604,800 18. 210 19. 50 20. 1,000 21. 132 22..07 23. 60,480 24. 43,243,200 25. 6,720 26. 336 27. 1,680 28. 20,160

3. Continued… 29. 8 30. 40,320 31. 40,320 32. 362,880 33. 1,814,400 34. 259,459,200 35. 13,366,080 36. 96,909,120 37. 271,252,800 38. 427,518,000 39. 720 40. 720 41. 60 42. 360 43. 10,080 44. 10,080 45. 151,200 46. 34,650 47. 908,107,200 48. 24

4. Continued…again… 49. 720 50. 24

5. Combinations

6. Essential Question: How do I solve problems involving combinations?

7. Formula:

8. Things you need to know: In a permutation, ORDER matters. In a combination, order does NOT matter. The value of combinations will be less than most permutations. You will use the nCr function in the calculator.

9. Problem Types: Determine the values for “n” (total number of objects) and “r” (the rate the objects are taken). “n” is always larger. Multiply the combinations together using the nCr key if there is more than one type of object. Find the probability of an event by dividing the product of individual combinations by the total number of combinations. Your answer is a %.

10. Example 1 Find the # of ways to purchase 3 different kinds of juice from a selection of 10 different juices. (The order in which they are chosen doesn’t matter, making this a combination). 10 C 3 = 120

11. Example 2 The difference between a permutation and a combination: COMBO: How many ways are there to choose a committee of 3 people from a group of 5? 5 C 3 = 10 Permutation: How many ways are there to choose 3 separate office holders (chairman, secretary, and treasurer) from a group of 5? 5 P 3 = 60

12. Example 3 How many different ways are there to purchase 2 CD’s, 3 cassettes, and 1 videotape from 7 CD titles, 5 cassette titles, and 3 videotape titles? 7 C 2 5 C 3 3 C 1 = 630

13. Example 4 In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. Find the probability that in a random sample of 6 respondents from this survey, exactly 2 favor the proposal regulation, and 4 oppose it..0537 = 5.4%

14. Assignment: Pg. 647, #’s 4-39a.

15. Pg. 647, 4-39a 4. 126 5. 220 / 1320 6. 2800 7. 7.6% 8. 35 9. 70 10. 120 11. 126 12. 9 13. 11 14. 1 15. 1 16. 75 17. 504 18..005 19..053 20. 10 21. 8 22. 495 23. 210 24. 225,792,840

16. Continued… 25. 15,504 26. 252 27. 378 28. 378 29. 252 30. 53.6% 31. 26.8% 32. 42.9% 33. 17.9% 34. Combo 35. Combo 36. Permutation 37. Permutation 38. Permutation 39. 2,598,960