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windsylph

  • 3 years ago

How many bit strings of length 10 contain exactly 5 bits equal to 1? Is it 2^10 - 2^5?

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  1. TuringTest
    • 3 years ago
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    I have no idea what this means :(

  2. TuringTest
    • 3 years ago
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    you have some number of bits of string length 10 and you want to know "how many contain 5 bits equal to 1" ?? what do you mean, 5 pieces of string equal to one what?

  3. windsylph
    • 3 years ago
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    Sorry, this was gotten straight from the problem statement. I'll rephrase this a little bit. How many 10-bit strings are there that have exactly five 1's in them?

  4. TuringTest
    • 3 years ago
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    @asnaseer can you lend a hand?

  5. windsylph
    • 3 years ago
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    the 1's can be in any nth bit. doesn't have to be next to each other :D

  6. TuringTest
    • 3 years ago
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    my impulse is to agree with you, 2^10-2^5, but combinatorics is not my strong suit

  7. windsylph
    • 3 years ago
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    Thank you. And it's alright. :D

  8. phi
    • 3 years ago
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    isn't it just 10 choose 5 ? \[\left(\begin{matrix}10 \\ 5\end{matrix}\right)=\frac{10!}{5! 5!}\]

  9. windsylph
    • 3 years ago
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    Hm. I'm a little bit fuzzy with combinations right now. 10 choose 5 because..?

  10. phi
    • 3 years ago
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    does this explain it? http://answers.yahoo.com/question/index?qid=20091122040726AAi6YU0

  11. phi
    • 3 years ago
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    Or http://answers.yahoo.com/question/index;_ylt=AhmQsH93Xi0bJtqIFdcUKLMCxgt.;_ylv=3?qid=20080504195059AAir3Ep the intuition is that you have 10 spaces all filled with 0's. You choose 5 of the zeros to be replaced with a 1. How many ways can we choose 5 out of 10 ? 10C5 is the standard answer

  12. windsylph
    • 3 years ago
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    haha I think that explanation suffices. thank you very much!

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