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4. Permutations and Combinations

  • Page ID
    21225
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    Contents 4A:

    1. Intro to Permutations (https://youtu.be/KC_1q9B_ZC8)
    2. Permutations, example 2 (https://youtu.be/rlnP0Fyzu4Y)
    3. Permutations, example 3 (https://youtu.be/jenG9qqv4wU)
    4. Permutation Notation and Guidelines (https://youtu.be/w40Ux--z3Q0)
    5. Permutations, example 4 (https://youtu.be/hosEvvBUJjY)
    6. Permutations with stages (https://youtu.be/4ItZ7KyTzSo)
    7. Permutations with cases and stages (https://youtu.be/r00rtKKtTTc)
    8. Permutations with complements (https://youtu.be/pnP6ODB1GUM)
    9. Rearrangements of Letters (https://youtu.be/gVp06_yOTLE)

     

     

     

    Example \(\PageIndex{1}\)

    Our classroom has 35 seats and 30 students. If any student could sit in any open seat, how many different seating arrangements are possible?

    Solution

    When the first student walks in, she has 35 options of where to sit. The second student then has 34 options remaining. The  third has 33, and so on. Therefore, the answer is \(P(35,30)\).

     

     

     

     

     

    Prework 4A:

    1. There are 8 runners in a race. In how many ways can gold, silver, and bronze medals be awarded? Please write your answer using permutation notation and also figure out a numerical value.
    2. An organization consisting of 8 females and 2 males meets to elect a president, secretary, and treasurer. In how many ways can the positions be filled? In how many ways can they be filled if both sexes must be represented?
    3. How many 10-letter “words” can be made from the word “antarctica”?

    Prework 4A Google form

    Contents 4B:

    1. Intro to Combinations (https://youtu.be/JL6SyzNLS6k)
    2. Combination Notation (https://youtu.be/2gb0K-w3Vw8)
    3. Combination or Permutation? (https://youtu.be/ejhH4J9Yg44)
    4. Combinations with Cases (https://youtu.be/jCWaLRF8V3c)
    5. Combinations with Stages (https://youtu.be/zAYTTRtCo38)
    6. Combinations with Complements (https://youtu.be/xAThjZFRcfM)

     

     

     

     

    The problem in the following video is solved in two ways: first using cases and stages, and then using complements.

     

    Prework 4B:

    1. Evaluate \(C(10,4)\).
    2. A student has volunteered to bring the chips for a pot-luck party. She is in a hurry and runs into a grocery store to get 3 different kinds of chips. There are 10 different kinds of chips on the shelf. How many ways can she choose the 3 bags of chips if they all have to be different kinds?
    3. Out of Sarah, Jennifer, Jason, and Quentin, I randomly select at least one person but at most three people to take the survey, how many groups could I choose?

    Prework 4B Google form

     


    4. Permutations and Combinations is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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