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## Homework Statement

prove that

[tex]\sum[/tex]

^{n}

_{k=0}([tex]^{n}_{k}[/tex]) ([tex]^{m-n}_{n-k}[/tex]) = ([tex]^{m}_{n}[/tex])

## Homework Equations

2

^{n}=[tex]\sum[/tex][tex]^{n}_{k=0}[/tex] ([tex]^{n}_{k}[/tex])

## The Attempt at a Solution

I know that every summand on the left hand side is a member of the power set times the combinations of it's complement and we can think of them in terms of the set changing with every possible combination, 1 element at a time and 2 at a time, 3 at a time, ..., n at a time. Or something like that... Definitely having trouble putting this into words let alone an equation. I certainly see the connection but am needing a little help on the proof. Please not the whole proof but just a little help putting it into words?

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