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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

 

asked in Combinatory by Veteran (66.1k points) 1148 2196 2522
retagged by | 662 views

2 Answers

+15 votes
Best answer

answer - D

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 by

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

answer is D
0 votes

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


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