0 votes 0 votes Determine the number of vectors $\{x_{1}...x_{n}\}$, such that each $x_{i}$ is either $0$ or $1$ and $\displaystyle{\sum_{i=1}^{n}x_{i}\geq k}$ Combinatory sheldon-ross combinatory + – Tesla! asked Feb 19, 2018 edited Mar 31, 2018 by Sukanya Das Tesla! 611 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Tesla! commented Feb 19, 2018 reply Follow Share I didn't understand the series nCk+ nCk+1 ... How did you derive it 0 votes 0 votes Jason commented Feb 19, 2018 reply Follow Share @Tesla! it should be $C(n,k) + C(n,k+1) + ........ + C(n,n)$. Where $C(n,k)$ is the number of vectors having exactly $k$ no of 1's. $C(n,k+1)$ is the number of vectors having exactly $k+1$ no of 1's. And so on. So it is $C(n,k) + C(n,k+1) + ........ + C(n,n)$. 0 votes 0 votes Tesla! commented Feb 19, 2018 reply Follow Share @jason @nitish got it thanks 0 votes 0 votes Please log in or register to add a comment.