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

1. TuringTest Group Title

I have no idea what this means :(

2. TuringTest Group Title

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 Group Title

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 Group Title

@asnaseer can you lend a hand?

5. windsylph Group Title

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

6. TuringTest Group Title

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

7. windsylph Group Title

Thank you. And it's alright. :D

8. phi Group Title

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

9. windsylph Group Title

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

10. phi Group Title