3 votes 3 votes How many 7 length bit strings have atleast 3 consecutive ones? Combinatory combinatory engineering-mathematics discrete-mathematic + – Balaji Jegan asked Jan 22, 2018 Balaji Jegan 1.1k views answer comment Share Follow See all 28 Comments See all 28 28 Comments reply Show 25 previous comments Balaji Jegan commented Jan 23, 2018 reply Follow Share Yes the answer is 47/128. I CHECKED MANUALLY FOR ALL THE 128 CASES. 0 votes 0 votes sourav. commented Jan 23, 2018 reply Follow Share @manu is right . I have got another method to solve it. $\text{7 length bit strings have atleast 3 consecutive ones}=\text{7 length bit strings possible-no 3 consecutive 1}$ $\text{# of bit string of length n with no 3 consecutive 1}T(n)=T(n-1)+T(n-2)+T(n-3)$ $T(0)=1,T(1)=2,T(2)=4$ solving $T(7)=81$ so reqd answer=$2^{7}-81=128-81=47$ 4 votes 4 votes rajatmyname commented Mar 13, 2019 reply Follow Share Is this formula still valid if question asks for n length bit strings having 3 consecutive ones only? 0 votes 0 votes Please log in or register to add a comment.
