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Math Help - n choose k question

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by absvalue View Post
    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.
    Have you stopped to think about this?
    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.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Have you stopped to think about this?
    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?
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