# Number of binary Strings Problem

• May 14th 2010, 05:07 AM
sid_178
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
• May 14th 2010, 05:44 AM
Plato
Quote:

Originally Posted by sid_178
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?
• May 14th 2010, 07:57 AM
sid_178
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 ?
• May 14th 2010, 08:09 AM
Plato
Quote:

Originally Posted by sid_178
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 $\binom{n+1}{k}$.