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## Main Question or Discussion Point

I was just wondering how you would prove the following:

[tex]\sum_{k=0}^{n}\frac{n!}{k!\left(n-k\right)!}=2^{n}[/tex]

Any help is appreciated.

[tex]\sum_{k=0}^{n}\frac{n!}{k!\left(n-k\right)!}=2^{n}[/tex]

Any help is appreciated.