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Math Help - Combinations Help

  1. #1
    Junior Member
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    Mar 2007
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    Post Combinations Help

    Hi, I'm stuck in these two problems. Can somebody help me? Thanks.

    1. I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?

    2. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
    How many ways can 4 toppings be selected where:

    a) All the toppings are vegetables. (I think this one is 70)
    b) All the toppings are meat.
    c) There is only cheese on the pizza
    d) There are 2 vegetables, 1 meat and 1 cheese
    e) There are 3 meats and 1 cheese.
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, cuteisa89!

    1. I've decided that the mentor group should be made up of 3 girls and 3 boys.
    Of the students who have A's 9 of them are girls and 6 are boys.
    How many ways can I form a group of 3 boys and 3 girls?
    To select the three girls, there are: C(9,3) = 84 ways.
    To select the three boys, there are: C(6,3) = 20 ways.

    Therefore, there are: .84 x 20 .= .1680 ways to choose the mentor group.



    2. A pizza shop offers the following toppings: 8 different vegetables,
    5 different meats, and 4 different cheeses.

    How many ways can 4 toppings be selected where:

    a) All the toppings are vegetables. (I think this one is 70) Yes!

    b) All the toppings are meat.
    Choose 4 of the 5 meats: .C(5,4) = 5 ways.

    c) There is only cheese on the pizza
    We choose four toppings and there are only four different cheeses.
    There is only one way ... choose all four of them.


    d) There are 2 vegetables, 1 meat and 1 cheese
    Choose two vegetables from the 8 available: .C(8,2) = 28 ways
    Choose one meat from the 5 meats: .5 ways
    Choose one cheese from the 4 cheeses: .4 ways
    . . Hence: .28 x 5 x 4 .= .560 ways


    e) There are 3 meats and 1 cheese.
    Choose 3 meats from the 5 meats: .C(5,3) = 10 ways
    Choose 1 cheese from the 4 cheeses: .4 ways
    . . Hence: .10 x 4 .= .40 ways

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