April 22, 2010Math 132: Foundations of Mathematics 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!) =

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Presentation transcript:

April 22, 2010Math 132: Foundations of Mathematics 11.2 Homework Solutions 8. 10! = 3,628, P 7 = 8,648, P 3 = 6, !/(2!2!) = 1,260

April 22, 2010Math 132: Foundations of Mathematics Amy Lewis Math Specialist IU1 Center for STEM Education

April 22, 2010Math 132: Foundations of Mathematics 11.2 Combinations Distinguish between permutations and combination problems. Solve problems involving combinations using the combinations formula.

April 22, 2010Math 132: Foundations of Mathematics 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?

April 22, 2010Math 132: Foundations of Mathematics 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)

April 22, 2010Math 132: Foundations of Mathematics 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

April 22, 2010Math 132: Foundations of Mathematics 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

April 22, 2010Math 132: Foundations of Mathematics 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

April 22, 2010Math 132: Foundations of Mathematics Formula for Combinations n C r = 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!

April 22, 2010Math 132: Foundations of Mathematics 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?

April 22, 2010Math 132: Foundations of Mathematics 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?

April 22, 2010Math 132: Foundations of Mathematics 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?

April 22, 2010Math 132: Foundations of Mathematics 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)!