Lesson 1 Nov 16 09
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Lesson 1 Nov 16 09

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Lesson 1 Nov 16 09 Presentation Transcript

  • 1. Counting A.K.A.  Combinatorics Heeley City Farm 014_edited­1 hopscotch by flickr user incurable_hippie
  • 2. In how many ways can 5 people be seated in a  straight line?
  • 3. A nickel and a quarter and a dime are tossed on a table.  Create a tree diagram to determine how many ways these  coins can land on the table. (The order in which the coins  land doesn't matter; it will next week.)
  • 4. The Fundamental Principle of Counting If there are M ways to do a first thing  and N ways to do a second thing, then  there are M x N ways to do both things. Example: How many outfits can be made from 3 pants and 4  shirts?
  • 5. In how many ways can six students be seated in  8 vacant seats?
  • 6. Factorial Notation Definition: n! = n•(n­1)•(n­2)•(n­3)• ......•3•2•1 0! = 1 Examples: 4! = 4•3•2•1 4! = 24 On the calculator: [MATH] [<] [4] Examples: 6! = 6•5•4•3•2•1 6! = 720
  • 7. Given the following  Solve for n n! = 5 (n­2)!
  • 8. Given (n+2)! Solve for n = 12 n!
  • 9. (a) How many “words” of 4 different letters  each can be made from the letters  A, E, I, O, R, S, T?
  • 10. (b) How many of these words begin with a  vowel and end with a consonant?
  • 11. (c) In how many of these words do vowels and  consonants alternate?
  • 12. Attachments Heeley City Farm 014_edited­1 hopscotch by flickr user incurable_hippie