Counting
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Counting . Chapter 13 sec 1. Break up into groups. One method of counting is using the tree diagram. It is useful to keep track of counting. Order of permutations does matter. You will determine all the possible ways to count. Remember order matters!!.

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Counting

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Counting

Counting

Chapter 13 sec 1


Counting

  • Break up into groups


Counting

  • One method of counting is using the tree diagram.

    • It is useful to keep track of counting.

    • Order of permutations does matter.


Counting

  • You will determine all the possible ways to count.

  • Remember order matters!!


Counting

  • How many ways can we do each of the following?

    • Flip a coin?

    • 2 ways; One head and one tails.


Counting

  • Roll a single die?

  • 6 ways

  • Pick a card from a standard deck of cards?

  • 52 ways


Counting

  • Example; How many ways can 3 coins be flipped?

    • How would you list the ways?

    • How would you list the possibilities?


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  • Make a tree diagram

  • 1st row is first coin

  • 2nd row is the second coin

  • 3rd row is the third coin.

  • You are listing out the possibilities.


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  • Begin

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HHH, HHT, HTH, HTT, TTH, TTT, THH, THT


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  • How about rolling two dice?

    • Let us say that one die is red and the other is green.


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  • In your group see if you can find all combinations.

  • Starting with

    • (1,1), (1,2), (1,3), …

    • 36 ways.


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  • If objects are allowed to be used more than once in a counting problem, we will use the phrase with repetition.

  • If we do not want objects to be used more than once, without repetition.


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  • Draw a tree diagram that illustrates the different ways to flip a dime, penny, quarter, and nickel.

  • 1. In how many ways can you get exactly one head?

  • 4


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  • 2. In how many ways can you get exactly two tails?

  • 6


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  • 3. How many different three-digit numbers can you form using the digits 1, 2, 5, 7, 8, & 9 without repetition?


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  • 120


Counting

  • You are a designer and has designed different tops, pants, and jackets to create outfits for a runway show. Without repetition, how many different outfits can your models wear if you had designed the following:

  • Seven tops, six pants, three jackets.


Counting

  • 126


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