# Number of binary Strings Problem

#### 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

#### Plato

MHF Helper
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?

#### 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 ?

#### Plato

MHF Helper
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 $$\displaystyle \binom{n+1}{k}$$.

sid_178