662 views

The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is

1. $^{n-1}C_k$

2. $^nC_k$

3. $^nC_{k+1}$

4. None of the above

retagged | 662 views

first place n zeroes side by side _ 0 _ 0 _ 0 ... 0 _

k 1's can be placed in any of the (n+1) available gaps hence number of ways  = n+1Ck

answered by Boss (9.3k points) 12 55 123
selected

Shouldn't the complete answer be n+1Ck  multiplied by k! multiplied by (k-1)!.taking into consideration the arrangements of 0 s

Arrangement of n zeroes can be in  Ways as

_0_0_....._0_

Keeping n+1 places for ones so that no two ones can be placed together and ther are k ones to be placed.

n+1Ck

all 0s and 1s are identical so no need to permutate them

Total no of ways = C(n+1 ,k)

The correct answer is (D) None of the above

answered by Boss (8.8k points) 3 8 12