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Do Now

Do Now . Find the number of permutations with 7 books taken 4 at a time. Find the number of permutations of the letters in each word: Tennessee Georgia Alabama. Pg. 640-641; 9-50 all. 4,920 696 2 2 56 210 20 720 604,800 210. 50 1,000 132 .07 60,480 43,243,200 6,720 336

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Do Now

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

  2. Pg. 640-641; 9-50 all • 4,920 • 696 • 2 • 2 • 56 • 210 • 20 • 720 • 604,800 • 210 • 50 • 1,000 • 132 • .07 • 60,480 • 43,243,200 • 6,720 • 336 • 1,680 • 20,160

  3. Continued… • 8 • 40,320 • 40,320 • 362,880 • 1,814,400 • 259,459,200 • 13,366,080 • 96,909,120 • 271,252,800 • 427,518,000 • 720 • 720 • 60 • 360 • 10,080 • 10,080 • 151,200 • 34,650 • 908,107,200 • 24

  4. Continued…again… • 720 • 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). • 10C3 = • 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? • 5C3 = 10 • Permutation: How many ways are there to choose 3 separate office holders (chairman, secretary, and treasurer) from a group of 5? • 5P3 = 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? 7C2 • 5C3 • 3C1 = 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 • 126 • 220 / 1320 • 2800 • 7.6% • 35 • 70 • 120 • 126 • 9 • 11 • 1 • 1 • 75 • 504 • .005 • .053 • 10 • 8 • 495 • 210 • 225,792,840

  16. Continued… • 15,504 • 252 • 378 • 378 • 252 • 53.6% • 26.8% • 42.9% • 17.9% • Combo • Combo • Permutation • Permutation • Permutation • 2,598,960

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