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Informal Geometry Period 1

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Title: Informal Geometry Period 1 Author: Cobb County School District Last modified by: install Created Date: 8/10/2006 9:39:48 PM Document presentation format – PowerPoint PPT presentation

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Title: Informal Geometry Period 1


1
Challenge of the Day
  • Bugs Bunny, Porky Pig, Tweety Bird, and Daffy
    Duck are going to the movies (they are best
    friends). How many different ways can they sit
    in seats A, B, C, and D below?
  • 2. Coach Elkins is picking a captain and
    co-captain from his 15 players. How many
    possibilities does he have if they are all
    equally likely?

24
A
B
C
D
210
2
Homework Review
3
GPS Algebra
UNIT QUESTION How do you use probability to make
plans and predict for the future? Standard
MM1D1-3 Todays Question What is the difference
between a permutation and combination? Standard
MM1D1.b.
4
Combinations
  • A selection of objects in which order is not
    important.
  • Example 8 people pair up to do an assignment.
    How many different pairs are there?

5
Combinations
  • AB AC AD AE AF AG AH
  • BA BC BD BE BF BG BH
  • CA CB CD CE CF CG CH
  • DA DB DC DE DF DG DH
  • EA EB EC ED EF EG EH
  • FA FB FC FD FE FG FH
  • GA GB GC GD GE GF GH
  • HA HB HC HD HE HF HG

6
Combinations
  • The number of r-combinations of a set with n
    elements,
  • where n is a positive integer and
  • r is an integer with 0 lt r lt n,
  • i.e. the number of combinations of r objects from
    n unlike objects is

7
Example 1
  • How many different ways are there to select two
    class representatives from a class of 20
    students?

8
Solution
  • The answer is given by the number of
    2-combinations of a set with 20 elements.
  • The number of such combinations is

9
Example 2
  • From a class of 24, the teacher is randomly
    selecting 3 to help her with a project. How many
    combinations are possible?

10
Your turn!
  • For your school pictures, you can choose 4
    backgrounds from a list of 10. How many
    combinations of backdrops are possible?

11
Your turn!
  • Venus Williams randomly selects 3 people out of
    her class of 20 to go to the courts and help her
    get ready for a tennis match. How many
    possibilities of people does she have?

12
Clarification on Combinations and Permutations
  • "My fruit salad is a combination of apples,
    grapes and bananas"
  • We don't care what order the fruits are in, they
    could also be "bananas, grapes and apples" or
    "grapes, apples and bananas", its the same fruit
    salad.

13
Clarification on Combinations and Permutations
  • "The combination to the safe is 472".
  • Now we do care about the order. "724" would not
    work, nor would "247". It has to be exactly
    4-7-2.

14
To sum it up
  • If the order doesn't matter, then it is a
    Combination.
  • If the order does matter, then it is a
    Permutation.
  • A Permutation is an ordered Combination.

15
Classwork Practice Worksheet
How many ways???
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