Number of binary Strings Problem

Sep 2008
14
0
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
 

Plato

MHF Helper
Aug 2006
22,462
8,634
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?
 
Sep 2008
14
0
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 ?
 

Plato

MHF Helper
Aug 2006
22,462
8,634
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 \(\displaystyle n\ge k-1\). Consider \(\displaystyle 10101\).
So yes it is \(\displaystyle \binom{n+1}{k}\).
 
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