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## Homework Statement

Show that: [tex](\stackrel{n}{k})=\#\left\{(\omega_{1},..., \omega_{n})\in\left\{0,1\right\}^{n}:\Sigma^{n}_{l=1}\omega_{l}=k\right\}[/tex]

(edit: the sigma is meant to go from l=1 to n)

## Homework Equations

It says to use this:

[tex](\stackrel{n}{k})=\#\left\{M\subseteq\left\{1,...,n\right\}:\#M=k\right\}[/tex]

## The Attempt at a Solution

First of all, I don't understand what {0,1}

^{n}is. Like, I think I should be able to nut this problem out if I understood that.. so I don't really need help with the actual question (yet :P), but I need help with the definition of {0,1}

^{n}.

The only thing I could find was [tex]\left\{0,1\right\}^{n}=\left\{(\omega_{1},...,\omega_{n}):\omega_{k}\in\left\{0,1\right\}, 1\leq k\leq n\right\}[/tex]

And I don't really get that...

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