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11.2 Homework Solutions

11.2 Homework Solutions. 8. 10! = 3,628,800 43. 13 P 7 = 8,648,640 44. 20 P 3 = 6,840 50. 7!/(2!2!) = 1,260. Math 132: Foundations of Mathematics. Amy Lewis Math Specialist IU1 Center for STEM Education. 11.2 Combinations.

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11.2 Homework Solutions

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  1. 11.2 Homework Solutions 8. 10! = 3,628,800 43. 13P7 = 8,648,640 44. 20P3 = 6,840 50. 7!/(2!2!) = 1,260 Math 132: Foundations of Mathematics

  2. Math 132:Foundations of Mathematics Amy Lewis Math Specialist IU1 Center for STEM Education Math 132: Foundations of Mathematics

  3. 11.2 Combinations • Distinguish between permutations and combination problems. • Solve problems involving combinations using the combinations formula. Math 132: Foundations of Mathematics

  4. Combinations • In June of 1999, Time magazine did a story on people whose careers became more profitable after their tragic deaths. • Kurt Cobain • Selena • James Dean • Jim Morrison • Marilyn Monroe • Of these 5 people, which 3 should be selected to be in a documentary on the topic? Math 132: Foundations of Mathematics

  5. Combinations • The items are selected from the same group. • The 5 stars who died tragically. • No item is used more than once. • You may adore Selena, but your 3 selections cannot be Selena, Selena, Selena. • The order of items makes no difference. • Morrison, Cobain, Selena is the same group as Selena, Cobain, Morrison) Math 132: Foundations of Mathematics

  6. Permutation or Combination? • Six students are running for student government president, vice president, and treasurer. How many different outcomes are possible for these three positions? PERMUTATION Math 132: Foundations of Mathematics

  7. Permutation or Combination? • Six people are on the board of supervisors for your neighborhood park. A 3-person committee is needed to study the possibility of expanding the park. How many different committees could be formed from the six people? COMBINATION Math 132: Foundations of Mathematics

  8. Permutation or Combination? • Baskin-Robbins offers 31 different flavors of ice cream. One of their items is a bowl consisting of 3 scoops of ice cream, each a different flavor. How many such bowls are possible? COMBINATION Math 132: Foundations of Mathematics

  9. Formula for Combinations • nCr = the number of combinations of n things taken r at a time. • Let’s look at the letters A, B, C, and D. • 24 permutations of 3 letters • 4 combinations of 3 letters n! (n – r)!r! Math 132: Foundations of Mathematics

  10. Using the Formula • You volunteer to pet-sit for your friend who has seven different animals. How many different pet combinations are possible if you take three of the seven pets? Math 132: Foundations of Mathematics

  11. Using the Formula • How many 5-card hands can be dealt from a deck that has 52 different cards? • How many different 4-card hands can be dealt from a deck that has 16 different cards? Math 132: Foundations of Mathematics

  12. Lottery Math • To win the lotto in the state of FL, one must correctly select 6 numbers from a collection of 53 numbers. The order in which the selection is made does not matter. How many different selections are possible? Math 132: Foundations of Mathematics

  13. Homework 626: 37 – 41 Be sure to think about whether the situation is an example of a permutation or combination. Next Session: Monday, April 26 Next week is a 3-session week (M, Th, F)! Math 132: Foundations of Mathematics

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