1. n choose k question

Question: How many n-digit binary (0,1) sequences contain exactly k 1s?

Could someone explain to me why the answer is n choose k? I don't understand it.

Thanks!

2. Originally Posted by absvalue
Question: How many n-digit binary (0,1) sequences contain exactly k 1s?
Could someone explain to me why the answer is n choose k? I don't understand it.
There is a string of n symbols, either a zero or a one.
So you have k places to put a one. So choose k from n.
Put zeros everywhere else.

3. Originally Posted by Plato
There is a string of n symbols, either a zero or a one.
So you have k places to put a one. So choose k from n.
Put zeros everywhere else.
Thanks for your explanation. I did think about it, but I've been having a hard time understanding the n choose k concept. So, if I understand this correctly...

"n choose k" is simply the number of possible ways to choose k items from a total of n?