math for the middle school and elementary teacher

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Which one of the following situations a permutation?
a) the number of ways 10 people can be lined up in a line for basketball tickets.
b) The number of possible four member bowling teams from a family of six siblings.
c) The number of ways to choose a committee of three from an eight member club.
d) The number of different fruit salads made by choosing out of seven fruits.
Is the answer d or b?

  • math for the middle school and elementary teacher -

    A permutation requires a specific order, such as a line-up, or a hierachy, such as as committee of president, vice-president, secretary and treasurer.
    In other words, order is important for a permutation.

    A combination is typically "n choose r", such as how many different pizzas if we choose 3 toppings out of 7, choose a 4 person committee, a 6-member hockey team (no captain), etc.

    If it is still not clear, please post a reply to that effect.

  • math for the middle school and elementary teacher -

    I think that the answer is d) the number of different fruit salads made by choosing four out of seven fruits because you can't have all of the same fruit in a fruit salad.

  • math for the middle school and elementary teacher -

    If the fruit salad A is made up of
    Cherries, pineapple, peach and grapes,
    and salad B is made up of
    Pineapple, peach, grapes and cherries.

    Is salad A different from salad B?
    If they are different (order is important), then (d) is a permutation.

  • math for the middle school and elementary teacher -

    They are not different but for a) the order doesn't matter for the way that the people can be lined up.

    But for b) order wouldn't matter either because there it doesn't matter who is on which team.

    Then c) there are no specifed posistions for the committee

    I'm stuck...

  • math for the middle school and elementary teacher -

    Is the line ABCD the same line as BADC,
    assuming the head of the line is the person on the left (A and B respectively)?

  • math for the middle school and elementary teacher -

    No, so that a) is the correct answer because order matters in the line! I am correct, right? Thank you very much:)

  • math for the middle school and elementary teacher -

    Yes, you're right, (a) is the correct answer because order matters.

  • math for the middle school and elementary teacher -

    Thank you! :)

  • math for the middle school and elementary teacher -

    You're welcome! :)

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