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Math Help - Choose question

  1. #1
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    Choose question

    I am working on some problems using binomial coefficients and am wondering if I am doing things correctly.

    One question...

    How many bit strings of length 10 either start with 000 or end with 1111?

    (10C3)(2)^7+(10C4)(2)^6

    I don't think that is correct because the order matters in this case right? Though I am not sure how to take that into account.
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  2. #2
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    Re: Choose question

    Quote Originally Posted by ehpoc View Post
    How many bit strings of length 10 either start with 000 or end with 1111?
    (10C3)(2)^7+(10C4)(2)^6
    Let A be the set of 10-bit strings 000\cdots.
    Let B be the set of 10-bit strings \cdots 1111.

    Now you want \|A\cup B\|=\|A\|+\| B\|-\|A\cap B\|.
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