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n bit strings are made by filling the digits 0 or 1.the number of strings in which there are exactly k zeroes with no two 0’s consecutive is

n bit strings are made by filling the digits 0 or 1.the number of strings in which there are exactly k zeroes with no two 0’s consecutive is
 

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
4 years ago
dear student, this s an ez ques. note that there would have to be m= n – k 1’s.
so, first of all arrange m 1’s in a row, and mark the spaces b/w the 1’s by crosses. also, mark the space next to the end 1’s by crosses too. so there are total (m – 1) + 2= m+1 crosses. now note that out of these m+1 crossed spaces, the k 0’s can be placed anywhere as they wouldnt be consecutive due to the presence of at least one 1.
hence the number of strings in which there are exactly k zeroes with no two 0’s consecutive= no of ways of placing 1’s * number of ways to select k places out of m+1 * number of ways of placing 0’s
= 1* m+1C* 1
n – k+1Ck
kindly approve :)

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