## windsylph 3 years ago How many bit strings of length 10 contain exactly 5 bits equal to 1? Is it 2^10 - 2^5?

1. TuringTest

I have no idea what this means :(

2. 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?

3. windsylph

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

@asnaseer can you lend a hand?

5. windsylph

the 1's can be in any nth bit. doesn't have to be next to each other :D

6. TuringTest

my impulse is to agree with you, 2^10-2^5, but combinatorics is not my strong suit

7. windsylph

Thank you. And it's alright. :D

8. phi

isn't it just 10 choose 5 ? $\left(\begin{matrix}10 \\ 5\end{matrix}\right)=\frac{10!}{5! 5!}$

9. windsylph

Hm. I'm a little bit fuzzy with combinations right now. 10 choose 5 because..?

10. phi

does this explain it? http://answers.yahoo.com/question/index?qid=20091122040726AAi6YU0

11. 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

12. windsylph

haha I think that explanation suffices. thank you very much!