anonymous
  • anonymous
How many bit strings of length 10 contain exactly 5 bits equal to 1? Is it 2^10 - 2^5?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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TuringTest
  • TuringTest
I have no idea what this means :(
TuringTest
  • TuringTest
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?
anonymous
  • anonymous
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?

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TuringTest
  • TuringTest
@asnaseer can you lend a hand?
anonymous
  • anonymous
the 1's can be in any nth bit. doesn't have to be next to each other :D
TuringTest
  • TuringTest
my impulse is to agree with you, 2^10-2^5, but combinatorics is not my strong suit
anonymous
  • anonymous
Thank you. And it's alright. :D
phi
  • phi
isn't it just 10 choose 5 ? \[\left(\begin{matrix}10 \\ 5\end{matrix}\right)=\frac{10!}{5! 5!}\]
anonymous
  • anonymous
Hm. I'm a little bit fuzzy with combinations right now. 10 choose 5 because..?
phi
  • phi
does this explain it? http://answers.yahoo.com/question/index?qid=20091122040726AAi6YU0
phi
  • phi
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
anonymous
  • anonymous
haha I think that explanation suffices. thank you very much!

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