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Splash Screen. Five-Minute Check (over Lesson 13–1) CCSS Then/Now New Vocabulary Key Concept: Factorial Example 1: Probability and Permutations of n Objects Key Concept: Permutations Example 2: Probability and n P r Key Concept: Permutations with Repetition

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 13–1) CCSS Then/Now New Vocabulary Key Concept: Factorial Example 1: Probability and Permutations of n Objects Key Concept: Permutations Example 2: Probability and nPr Key Concept: Permutations with Repetition Example 3: Probability and Permutations with Repetition Key Concept: Circular Permutations Example 4: Probability and Circular Permutations Key Concept: Combinations Example 5: Probability and nCr Lesson Menu

  3. Which is not part of the sample space for the following situation? George can eat at two different restaurants on his college campus. He has an hour break at 11:00 and at 1:00. A. R1, 11 B. R1, R2 C. R2, 1 D. R2, 11 5-Minute Check 1

  4. Which is not part of the sample space for the following situation? An editor has two writers available to write a story. They can either write a factual piece or an editorial. A. W1, E B. W2, E C. E, F D. W1, F 5-Minute Check 2

  5. Find the number of possible outcomes for the situation. When choosing a cell phone, Terrence has 4 color choices and 5 additional options. A. 9 B. 15 C. 20 D. 40 5-Minute Check 3

  6. Find the number of possible outcomes for the situation. In a cafeteria there are 4 choices for a main dish, 4 choices for a side dish, 5 choices of drinks, and 2 choices for dessert. A. 40 B. 120 C. 150 D. 160 5-Minute Check 4

  7. For her birthday, Trina received a new wardrobe consisting of 6 shirts, 4 pairs of pants, 2 skirts,and 3 pairs of shoes. How many new outfits can she make? A. 144 B. 130 C. 94 D. 72 5-Minute Check 5

  8. Content Standards S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. Mathematical Practices 1 Make sense of problems and persevere in solving them. 4 Model with mathematics. CCSS

  9. You used the Fundamental Counting Principle. • Use permutations with probability. • Use combinations with probability. Then/Now

  10. permutation • factorial • circular permutation • combination Vocabulary

  11. Concept

  12. Probability and Permutations of n Objects TALENT SHOW Eli and Mia, along with 30 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Eli will be called to perform first and Mia will be called second? Step 1 Find the number of possible outcomes in the sample space. This is the number of permutations of the order of the 30 contestants, or 30!. Step 2 Find the number of favorable outcomes. This is the number of permutations of the other contestants given that Eli is first and Mia is second, which is (30 – 2)! or 28!. Example 1

  13. Answer: Probability and Permutations of n Objects Step 3 Calculate the probability. number of favorable outcomes number of possible outcomes 1 Expand 30! and divide out common factors. 1 Simplify. Example 1

  14. A. B. C. D. Hila, Anisa, and Brant are in a lottery drawing for housing with 40 other students to choose their dorm rooms. If the students are chosen in random order, what is the probability that Hila is chosen first, Anisa second, and Brant third? Example 1

  15. Concept

  16. Probability and nPr There are 12 puppies for sale at the local pet shop. Four are brown, four are black, three are spotted, and one is white. What is the probability that all the brown puppies will be sold first? Step 1 Since the order that the puppies are sold is important, this problem relates to permutation. The number of possible outcomes in the sample space is the number of permutations of 12 puppies taken 4 at a time. 1 1 Example 2

  17. Step 3 So the probability of the four brown puppies being sold first is Answer: Probability and nPr Step 2 The number of favorable outcomes is the number of permutations of the 4 brown puppies in their specific positions. This is 4! or 24 favorable outcomes. Example 2

  18. A. B. C. D. There are 24 people in a hula-hoop contest. Five of them are part of the Garcia family. If everyone in the contest is equally as good at hula-hooping, what is the probability that the Garcia family finishes in the top five spots? Example 2

  19. Concept

  20. Probability and Permutations with Repetition TILES A box of floor tiles contains 5 blue (bl) tiles, 2 gold (gd) tiles, and 2 green (gr) tiles in random order. The desired pattern is bl, gd, bl, gr, bl, gd, bl, gr, and bl. If you selected a permutation of these tiles at random, what is the probability that they would be chosen in the correct sequence? Step 1 There is a total of 9 tiles. Of these tiles, blue occurs 5 times, gold occurs 2 times, and green occurs 2 times. So the number of distinguishable permutations of these tiles is Use acalculator. Example 3

  21. Step 3 The probability that a permutation of these tiles selected will be in the chosen sequence is Answer: Probability and Permutations with Repetition Step 2 There is only one favorable arrangement—bl, gd, bl, gr, bl, gd, bl, gr, bl. Example 3

  22. A.B. C.D. TILES A box of floor tiles contains 3 red (rd) tiles, 3 purple (pr) tiles, and 2 orange (or) tiles in random order. The desired patter is rd, rd, pr , pr, or, rd, pr, and or. If you selected a permutation of these tiles at random, what is the probability that they would be chosen in the correct sequence? Example 3

  23. Concept

  24. Probability and Circular Permutations A. SEATINGIf 8 students sit at random in the circle of chairs shown, what is the probability that the students sit in the arrangement shown? Explain your reasoning. Since there is no fixed reference point, this is a circular permutation. So there are (8 – 1)! or 7! distinguishable permutations of the way the students can sit. Example 4

  25. Answer:The probability of the students sitting in the arrangement shown is Probability and Circular Permutations Example 4

  26. Since the crayons are packaged in a row, instead of a circle with no fixed reference point, this is a linear permutation. In that case, since there are 8 positions and 1 red crayon, the probability that the crayon on the far left is red is Answer: Probability and Circular Permutations B. CRAYONSYou purchase a box of 8 crayons. If the crayons are packaged in random order, what is the probability that the crayon on the far left is red? Explain your reasoning. Example 4

  27. A.B. C.D. A. TABLE SETTINGS If for a birthday party there are 5 people having cake, and there are 5 different colored plates, what is the probability that if chosen at random the plates will be displayed as seen in the order at the right? Example 4

  28. A.B. C. D. B. CONSTRUCTION A home builder is constructing 6 different models of homes on a major cross street, 5 of which are 2-floored homes, and only 1 home that is 1 floor. If built at random, what is the possibility the 1-floored home will be on the 1st plot of land? Example 4

  29. Concept

  30. Probability and nCr A set of alphabet magnets are placed in a bag. If 5 magnets are drawn from the bag at random, what is the probability that they will be the letters a, e, i, o, and u? Step 1 Since the order in which the magnets are chosen does not matter, the number of possible outcomes in the sample space is the number of combinations of 26 letters taken 5 at a time, 26C5. Example 5

  31. Step 3 So, the probability of just getting a, e, i, o, and u is Answer: Probability and nCr Step 2 There is only one favorable outcome that all 5 letters are a, e, i, o, and u. The order in which they are chosen is not important. Example 5

  32. A. ans B. ans C. ans D. ans A set of alphabet magnets are placed in a bag. If 4 magnets are drawn from the bag at random, what is the probability that they will be the letters m, a, t, and h? Example 5

  33. End of the Lesson

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