Informal Geometry Period 1

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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.
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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?

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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

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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

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Example 1

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

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Solution

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

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Example 2

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

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Your turn!

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

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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?

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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.

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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.

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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.

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Classwork Practice Worksheet
How many ways???