1. Modeling Monday Follow Up The actual count of trees! TeacherOld TreesNew Trees Loggins1282655 Fox1280660 Lindahl1274641 Averages:1279652

2. 12.4 Permutations

3. Permutations group of elements with order – ex: zip codes, phone #s key words: – arrange – order – assign order matters!

4. Remember?? I have 5 positions and 5 people to fill the positions Make 5 blanks: 54 ∙ = 5! 321 ∙∙∙ = 120

5. I have 4 people to choose from to fill 2 positions Make 2 blanks: For 2 nd slot? 4How many choices for 1 st slot? 3 43= 12 ∙

6. Permutations Formula Formula: # of people to choose from # you are arranging Memorize!!

7. Permutations Formula Last example using formula: (4 people to choose from to fill 2 positions) can put in calc

8. Remember: 8 cars parallel parked along one side of street. How many ways can all 8 be arranged? Three diff ways to solve: 1)8! 3) 6 87 ∙ = 40, 320 2) 5 4 ∙ 3 ∙ 21 ∙ ∙∙∙

9. How many if only 5 cars out of 8 arranged? 2 diff ways to solve: 2) 6 87 ∙ 1) 5 4 ∙∙ ∙= 6720

10. Example: If we have 8 books, how many ways can we arrange 3 on a bookshelf? Two methods: OR 876∙ ∙ = 336

11. Probability of getting a Permutation a) How many possible perms are there? 5!= 120 A 5-letter perm. is selected at random from the letters GRATE. =24 b) How many of these perms BEGINS with G? 1 4 32 1 c) What’s the prob. the perm BEGINS with G?

12. Probability of getting a Permutation A 5-letter perm. is selected at random from the letters GRATE. =6 3 1 21 1 d) What’s the prob. the 2 nd letter is a T and last is a G? e) What’s the prob. the 2 nd letter is a consonant and last is a E?

13. TOO: 11 girls try out for Varsity soccer. a) In how many ways could the 11 positions be filled if there are no restrictions? b) In how many ways can the positions be filled if Mabel must be goalie? c) What’s the prob. that Mabel is goalie? d) What’s the prob. that Mabel, Sue or Deb is goalie? e) What’s the prob. that Mabel, Sue or Deb is goalie and Alice or Pat is center forward?

14. Arranging letters in a word with repeats MISSISSIPPI Total letters Count repeating letters: 4 - I’s Total letters: 11 4 - S’s2 - P’s Divide by # of each repeat = 34, 650

15. T.O.O. Arranging letters in a word with repeats FOOTBALL Total letters Repeating letters: 2 - O’s Total letters: 8 2 - L’s Divide by # of each repeat = 10,080

16. Homework Pg. 647-650 # 1-17 odd, 20, 21