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Math Help - Basic Counting Methods

  1. #1
    DBA
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    Basic Counting Methods

    The question is
    How many integers are between 0 and 40? my answer 41
    How many of these integers are divisible by 2? my anser 20

    How many unordered pairs of these integers are whose difference is 5?

    Here I do not know where to start? An unordered pair is {#1, #2}, so I think I have two sets of numbers
    set one are all numbers possible for #1 and
    set two are all numbers possible for #2

    First I am not sure how to treat the sets, because the pairs are unordered. So, What I understand is that in the first place could be a 30 and in the second a 5 or the other way around.

    Then, I do not know how to express the "difference is 5"

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by DBA View Post
    The question is
    How many integers are between 0 and 40? my answer 41
    How many of these integers are divisible by 2? my anser 20
    Has either your instructor or your textbook discussed the meaning of between?
    The way either uses that word will change the answer to the first question.
    For example, I do not consider 0 to be between 0 & 40.
    It is clear that 5 is between 0 & 40, but 40 is not.
    However, I have seen people who do disagree with me.
    I know in test prep writing one uses the pharse ‘from 0 to 40’ if we intend inclusion.
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  3. #3
    DBA
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    Between to numbers include the numbers at the edges. So 0 to 40, includes the 0 and the 40 in my textbook.
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  4. #4
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    Quote Originally Posted by DBA View Post
    Between to numbers include the numbers at the edges. So 0 to 40, includes the 0 and the 40 in my textbook.
    O.K. So we have a list of integers from 0 to 40.

    Quote Originally Posted by DBA View Post
    The question is
    How many unordered pairs of these integers are whose difference is 5
    The 'smallest' unordered pair is \{0,5\}.
    The largest is \{35,40\}.
    Another such pair is \{8,13\}.
    So how many altogether?
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  5. #5
    DBA
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    So for my first number of the pair I have numbers from 0 to 35, which are 36 possibilities and for the second number of the pair I have numbers from 5 to 40, which are 36 possibilities.
    My total possibilities to combine them would be 36*36. is that correct?

    Would that include that I can have a pair like {13,8}? Since it is unordered the order should not matter, right?
    Thanks
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  6. #6
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    Quote Originally Posted by DBA View Post
    So for my first number of the pair I have numbers from 0 to 35, which are 36 possibilities and for the second number of the pair I have numbers from 5 to 40, which are 36 possibilities.
    My total possibilities to combine them would be 36*36. is that correct?
    Would that include that I can have a pair like {13,8}? Since it is unordered the order should not matter, right?
    Why in the world would you square the number?
    An unordered pair is simply a set of two terms.
    So \{13,8\}=\{8,13\}, one unordered pair.
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  7. #7
    DBA
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    mmh a wrong thought I guess. I wrote them out and now it is clear that there are 36 combinations possible. Thanks for your help!
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