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Math Help - Inclusion and exclusion question

  1. #1
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    Inclusion and exclusion question

    Hi
    I have the following question and struggling:
    let A be the 10-digit decimal integer, that is
    A:={0000000000,0000000001,...,9999999999}
    How many elements of A have exactly three o's and two 1's?

    So i need to use p(a and b)= p(a) + p(b) - p(a or b)
    Just struggling to find how many elements there are with exactly what is needed so i can apply it to the equation
    many thanks in advance.
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  2. #2
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    How many elements of A have exactly three o's and two 1's?
    Three 0's and two 1's make 5, not 10, digits. Also, |A union B| = |A| + |B| - |A intersection B|. I think you have "and" and "or" switched.
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  3. #3
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    Quote Originally Posted by emakarov View Post
    Three 0's and two 1's make 5, not 10, digits. Also, |A union B| = |A| + |B| - |A intersection B|. I think you have "and" and "or" switched.
    I think its asking how many combinations are there of exactly 3 o's for example 9999999000 is possible etc and then them same for exactly two 1's, something to do with combinations just can't put my finger on it.
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  4. #4
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    Quote Originally Posted by breitling View Post
    let A be the 10-digit decimal integer, that is
    A:={0000000000,0000000001,...,9999999999}
    How many elements of A have exactly three o's and two 1's?
    There will be five places for digits other than a 0 or a 1.
    Select those places \binom{10}{5}. Those can be filled in 8^5 different ways.
    From the remaining five places choose two, \binom{5}{2}, into which the 1ís go. The zeros go into the remaining places.
    Now just multiply.

    Edit: Note the and.
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