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Math Help - Number of binary Strings Problem

  1. #1
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    Number of binary Strings Problem

    The number of binary strings of n zeroes and k ones that no two ones are adjacent are :

    (a)n-1Ck

    (b)n+1Ck

    (c)nCk

    d)k+n-1Ck
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  2. #2
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    Quote Originally Posted by sid_178 View Post
    The number of binary strings of n zeroes and k ones that no two ones are adjacent are :
    (a)n-1Ck (b)n+1Ck (c)nCk d)k+n-1Ck
    This is a good problem.
    What do you thin the answer is and why?
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  3. #3
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    By Assumption ,say ,n>k..
    Now ,if we keep n zeroes ..we have n+1 places out of which we can keep k ones
    in n+1ck ways .Is that right ?
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  4. #4
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    Quote Originally Posted by sid_178 View Post
    By Assumption ,say ,n>k..
    Now ,if we keep n zeroes ..we have n+1 places out of which we can keep k ones in n+1ck ways .Is that right ?
    Actually we assume that n\ge k-1. Consider 10101.
    So yes it is \binom{n+1}{k}.
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