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P.O.D. #6

P.O.D. #6. basic. advanced. How many total outcomes are there when selecting one sweatshirt from a choice of five sweatshirts and one pair of pants from a choice of four pairs of pants?.

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P.O.D. #6

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  1. P.O.D. #6 basic advanced How many total outcomes are there when selecting one sweatshirt from a choice of five sweatshirts and one pair of pants from a choice of four pairs of pants? A movie theater offers a combo special with 3 different drink sizes (S, M, L) and 3 different popcorn sizes (S, M, L). What is the probability that the next customer will order combo with a small drink and a small popcorn? 5  4 = 20 3  3 = 9 1 9 P(SS) =

  2. Permutations

  3. A permutation is an arrangement, or listing, of objects in which order is important. You can use the Fundamental Counting Principle to find the number of permutations.

  4. Example: How many ways can four different books be arranged on a shelf? Total Combos 2nd Book 3rd Book 4th Book 1st Book = × × × 3 4 2 1 24

  5. Example: An ice cream shop has 31 flavors. Carlos wants to buy a three-scoop cone with three different flavors. How many cones could he buy if the order of the flavors is important? Total Combos 1st Scoop 2nd Scoop 3rd Scoop = × × 31 30 29 26,970

  6. Permutations can be used when finding the probability of an event. Example: Two different letters are randomly selected from the letters in the word hornet. What is the probability that the first letter selected is h and the second is t? Total Outcomes 1st Letter 2nd Letter 1 30 P(ht) = = × 6 5 30

  7. Whiteboard: In the Battle of the Bands contest, in how many ways can the four participating bands perform? 1st band  2nd band  3rd band  4th band = Total Outcomes 4  3  2  1 = 24

  8. Whiteboard: You have five seasons of your favorite TV show on DVD. If you randomly select two of them from a shelf, what is the probability that you will select season one first and season two second? 1st Selection  2nd Selection = Total Outcomes 5 4 = 20 1 20 P(1stthen 2nd season) =

  9. Notation The symbol P(31, 3) represents the number of permutations of 31 things taken 3 at a time. Start with 31 P(31, 3) = 31  30  29 Use three factors.

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