Sheldon Ross

Question

Determine the number of vectors $\{x_{1}...x_{n}\}$, such that each $x_{i}$ is either $0$ or $1$ and

$\displaystyle{\sum_{i=1}^{n}x_{i}\geq k}$

Comments

I didn't understand the series

nCk+ nCk+1 ...

How did you derive it

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@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 $C(n,k) + C(n,k+1) + ........ + C(n,n)$.

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@jason @nitish got it thanks