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Math Help - help me which counting is correct

  1. #1
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    help me which counting is correct

    How many strings are there of four lowercase letters that have the letter x in them?
    which of the following answer is correct?
    1) 1x26x26x26 = 26^3 = 17576
    2) 26^4 - 25^4 = 66351

    please explain me
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  2. #2
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    Quote Originally Posted by zpwnchen View Post
    How many strings are there of four lowercase letters that have the letter x in them?
    which of the following answer is correct?
    1) 1x26x26x26 = 26^3 = 17576
    2) 26^4 - 25^4 = 66351

    please explain me
    26^4 - 25^4 = 66351 is the number of four letters strings which contain at least one x.
    Is that what the question means.

    (4)25^3 = 62500 is the number of four letters strings which contain exactly one x.
    Last edited by Plato; October 31st 2009 at 02:38 PM.
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  3. #3
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    Quote Originally Posted by Plato View Post
    (4)25^3 = 62500 is the number of four letters strings which contain exactly one x.
    can you tell me why you multiply with 4? what is the concept behind?
    Last edited by Plato; October 31st 2009 at 02:38 PM.
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  4. #4
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    You multiply by 4 because you have 4 ways to place x:

    x _ _ _
    _ x _ _
    _ _ x _
    _ _ _ x
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  5. #5
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    Quote Originally Posted by zpwnchen View Post
    can you tell me why you multiply with 4? what is the concept behind?
    Please note my edit.
    There are four places to put the one x.
    Last edited by Plato; October 31st 2009 at 03:56 PM.
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  6. #6
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    that makes sense! thank you
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