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Math Help - Combination problems

  1. #1
    Newbie ilovepsycho's Avatar
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    Combination problems

    1. It takes five people working on different tasks to produce a new product. A small workplace has five
    different workers and the plant manager wants to experimentally compare which workers/job
    combinations produce the product in the fastest time. If they wanted to perform this experiment, how
    many different combinations must they analyze?


    My answer is 5 x 5 = 25.
    Is that correct? Your check is needed.

    2. Domino’s Pizza offers pizzas with two different sizes, three different types of crusts and up to 10
    toppings. For topping you have a choice of having or not having.
    How many different types of pizzas can be made?


    My answer to the 2nd question is 2 x 3 x 11 = 66.
    I that also correct? Your check is needed.
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  2. #2
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    For the first question:
    I think you need to use the multiplication principle. The first task could be filed by 5 people then the second task by 4 then the third task by 3 and so on.
    It would be 5 x 4 x 3 x 2 x 1.

    For the second question.
    I think you have the correct answer.
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  3. #3
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    Quote Originally Posted by ilovepsycho View Post
    2. Domino’s Pizza offers pizzas with two different sizes, three different types of crusts and up to 10
    toppings. For topping you have a choice of having or not having.
    How many different types of pizzas can be made?

    My answer to the 2nd question is 2 x 3 x 11 = 66.
    If we read that bit about 'toppings' to mean we can any or all or none the the answer is 2\times 3\times 2^{10}.
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  4. #4
    Newbie ilovepsycho's Avatar
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    Quote Originally Posted by Plato View Post
    If we read that bit about 'toppings' to mean we can any or all or none the the answer is 2\times 3\times 2^{10}.
    Why did you multiply 2^{10}? Please explain to me.
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  5. #5
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    Quote Originally Posted by ilovepsycho View Post
    Why did you multiply 2^{10}? Please explain to me.
    The exclamation depends on how one reads “up to 10 toppings. For topping you have a choice of having or not having.”
    If that means that the pizza has no topping or exactly one topping then your 11 is correct.
    However, if it means we can choose any combinations of toppings from none to all ten (I think this is what is meant from the wording) then we can have any subset of the toppings.
    From a set of ten items there are 2^{10} possible subsets.
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  6. #6
    Newbie ilovepsycho's Avatar
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    Quote Originally Posted by Plato View Post
    The exclamation depends on how one reads “up to 10 toppings. For topping you have a choice of having or not having.”
    If that means that the pizza has no topping or exactly one topping then your 11 is correct.
    However, if it means we can choose any combinations of toppings from none to all ten (I think this is what is meant from the wording) then we can have any subset of the toppings.
    From a set of ten items there are 2^{10} possible subsets.
    You are a genius! My professor said to his students that what you are talking to me is RIGHT! Thus, Your calculation is correct, 2 x 3 x 2^10
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